diff --git a/starlette/_utils.py b/starlette/_utils.py
index 26854f3d4..15ccd92a4 100644
--- a/starlette/_utils.py
+++ b/starlette/_utils.py
@@ -1,9 +1,12 @@
 import asyncio
 import functools
+import re
 import sys
 import typing
 from contextlib import contextmanager
 
+from starlette.types import Scope
+
 if sys.version_info >= (3, 10):  # pragma: no cover
     from typing import TypeGuard
 else:  # pragma: no cover
@@ -86,3 +89,9 @@ def collapse_excgroups() -> typing.Generator[None, None, None]:
                 exc = exc.exceptions[0]  # pragma: no cover
 
         raise exc
+
+
+def get_route_path(scope: Scope) -> str:
+    root_path = scope.get("root_path", "")
+    route_path = re.sub(r"^" + root_path, "", scope["path"])
+    return route_path
diff --git a/starlette/datastructures.py b/starlette/datastructures.py
index a0c3ba140..e12957f50 100644
--- a/starlette/datastructures.py
+++ b/starlette/datastructures.py
@@ -30,7 +30,7 @@ def __init__(
             assert not components, 'Cannot set both "scope" and "**components".'
             scheme = scope.get("scheme", "http")
             server = scope.get("server", None)
-            path = scope.get("root_path", "") + scope["path"]
+            path = scope["path"]
             query_string = scope.get("query_string", b"")
 
             host_header = None
diff --git a/starlette/middleware/wsgi.py b/starlette/middleware/wsgi.py
index 95578c9d2..2ce83b074 100644
--- a/starlette/middleware/wsgi.py
+++ b/starlette/middleware/wsgi.py
@@ -20,10 +20,16 @@ def build_environ(scope: Scope, body: bytes) -> typing.Dict[str, typing.Any]:
     """
     Builds a scope and request body into a WSGI environ object.
     """
+
+    script_name = scope.get("root_path", "").encode("utf8").decode("latin1")
+    path_info = scope["path"].encode("utf8").decode("latin1")
+    if path_info.startswith(script_name):
+        path_info = path_info[len(script_name) :]
+
     environ = {
         "REQUEST_METHOD": scope["method"],
-        "SCRIPT_NAME": scope.get("root_path", "").encode("utf8").decode("latin1"),
-        "PATH_INFO": scope["path"].encode("utf8").decode("latin1"),
+        "SCRIPT_NAME": script_name,
+        "PATH_INFO": path_info,
         "QUERY_STRING": scope["query_string"].decode("ascii"),
         "SERVER_PROTOCOL": f"HTTP/{scope['http_version']}",
         "wsgi.version": (1, 0),
diff --git a/starlette/requests.py b/starlette/requests.py
index 83a52aca1..e51223bab 100644
--- a/starlette/requests.py
+++ b/starlette/requests.py
@@ -99,9 +99,18 @@ def url(self) -> URL:
     def base_url(self) -> URL:
         if not hasattr(self, "_base_url"):
             base_url_scope = dict(self.scope)
-            base_url_scope["path"] = "/"
+            # This is used by request.url_for, it might be used inside a Mount which
+            # would have its own child scope with its own root_path, but the base URL
+            # for url_for should still be the top level app root path.
+            app_root_path = base_url_scope.get(
+                "app_root_path", base_url_scope.get("root_path", "")
+            )
+            path = app_root_path
+            if not path.endswith("/"):
+                path += "/"
+            base_url_scope["path"] = path
             base_url_scope["query_string"] = b""
-            base_url_scope["root_path"] = base_url_scope.get("root_path", "")
+            base_url_scope["root_path"] = app_root_path
             self._base_url = URL(scope=base_url_scope)
         return self._base_url
 
diff --git a/starlette/routing.py b/starlette/routing.py
index 0ced9e667..d718bb921 100644
--- a/starlette/routing.py
+++ b/starlette/routing.py
@@ -10,7 +10,7 @@
 from enum import Enum
 
 from starlette._exception_handler import wrap_app_handling_exceptions
-from starlette._utils import is_async_callable
+from starlette._utils import get_route_path, is_async_callable
 from starlette.concurrency import run_in_threadpool
 from starlette.convertors import CONVERTOR_TYPES, Convertor
 from starlette.datastructures import URL, Headers, URLPath
@@ -255,9 +255,8 @@ def __init__(
     def matches(self, scope: Scope) -> typing.Tuple[Match, Scope]:
         path_params: "typing.Dict[str, typing.Any]"
         if scope["type"] == "http":
-            root_path = scope.get("route_root_path", scope.get("root_path", ""))
-            path = scope.get("route_path", re.sub(r"^" + root_path, "", scope["path"]))
-            match = self.path_regex.match(path)
+            route_path = get_route_path(scope)
+            match = self.path_regex.match(route_path)
             if match:
                 matched_params = match.groupdict()
                 for key, value in matched_params.items():
@@ -345,9 +344,8 @@ def __init__(
     def matches(self, scope: Scope) -> typing.Tuple[Match, Scope]:
         path_params: "typing.Dict[str, typing.Any]"
         if scope["type"] == "websocket":
-            root_path = scope.get("route_root_path", scope.get("root_path", ""))
-            path = scope.get("route_path", re.sub(r"^" + root_path, "", scope["path"]))
-            match = self.path_regex.match(path)
+            route_path = get_route_path(scope)
+            match = self.path_regex.match(route_path)
             if match:
                 matched_params = match.groupdict()
                 for key, value in matched_params.items():
@@ -420,9 +418,8 @@ def routes(self) -> typing.List[BaseRoute]:
     def matches(self, scope: Scope) -> typing.Tuple[Match, Scope]:
         path_params: "typing.Dict[str, typing.Any]"
         if scope["type"] in ("http", "websocket"):
-            path = scope["path"]
-            root_path = scope.get("route_root_path", scope.get("root_path", ""))
-            route_path = scope.get("route_path", re.sub(r"^" + root_path, "", path))
+            root_path = scope.get("root_path", "")
+            route_path = get_route_path(scope)
             match = self.path_regex.match(route_path)
             if match:
                 matched_params = match.groupdict()
@@ -432,11 +429,20 @@ def matches(self, scope: Scope) -> typing.Tuple[Match, Scope]:
                 matched_path = route_path[: -len(remaining_path)]
                 path_params = dict(scope.get("path_params", {}))
                 path_params.update(matched_params)
-                root_path = scope.get("root_path", "")
                 child_scope = {
                     "path_params": path_params,
-                    "route_root_path": root_path + matched_path,
-                    "route_path": remaining_path,
+                    # app_root_path will only be set at the top level scope,
+                    # initialized with the (optional) value of a root_path
+                    # set above/before Starlette. And even though any
+                    # mount will have its own child scope with its own respective
+                    # root_path, the app_root_path will always be available in all
+                    # the child scopes with the same top level value because it's
+                    # set only once here with a default, any other child scope will
+                    # just inherit that app_root_path default value stored in the
+                    # scope. All this is needed to support Request.url_for(), as it
+                    # uses the app_root_path to build the URL path.
+                    "app_root_path": scope.get("app_root_path", root_path),
+                    "root_path": root_path + matched_path,
                     "endpoint": self.app,
                 }
                 return Match.FULL, child_scope
@@ -787,15 +793,12 @@ async def app(self, scope: Scope, receive: Receive, send: Send) -> None:
             await partial.handle(scope, receive, send)
             return
 
-        root_path = scope.get("route_root_path", scope.get("root_path", ""))
-        path = scope.get("route_path", re.sub(r"^" + root_path, "", scope["path"]))
-        if scope["type"] == "http" and self.redirect_slashes and path != "/":
+        route_path = get_route_path(scope)
+        if scope["type"] == "http" and self.redirect_slashes and route_path != "/":
             redirect_scope = dict(scope)
-            if path.endswith("/"):
-                redirect_scope["route_path"] = path.rstrip("/")
+            if route_path.endswith("/"):
                 redirect_scope["path"] = redirect_scope["path"].rstrip("/")
             else:
-                redirect_scope["route_path"] = path + "/"
                 redirect_scope["path"] = redirect_scope["path"] + "/"
 
             for route in self.routes:
diff --git a/starlette/staticfiles.py b/starlette/staticfiles.py
index 895105a7d..0101b11bc 100644
--- a/starlette/staticfiles.py
+++ b/starlette/staticfiles.py
@@ -1,6 +1,5 @@
 import importlib.util
 import os
-import re
 import stat
 import typing
 from email.utils import parsedate
@@ -8,6 +7,7 @@
 import anyio
 import anyio.to_thread
 
+from starlette._utils import get_route_path
 from starlette.datastructures import URL, Headers
 from starlette.exceptions import HTTPException
 from starlette.responses import FileResponse, RedirectResponse, Response
@@ -110,9 +110,8 @@ def get_path(self, scope: Scope) -> str:
         Given the ASGI scope, return the `path` string to serve up,
         with OS specific path separators, and any '..', '.' components removed.
         """
-        root_path = scope.get("route_root_path", scope.get("root_path", ""))
-        path = scope.get("route_path", re.sub(r"^" + root_path, "", scope["path"]))
-        return os.path.normpath(os.path.join(*path.split("/")))  # type: ignore[no-any-return]  # noqa: E501
+        route_path = get_route_path(scope)
+        return os.path.normpath(os.path.join(*route_path.split("/")))  # noqa: E501
 
     async def get_response(self, path: str, scope: Scope) -> Response:
         """
diff --git a/tests/middleware/test_wsgi.py b/tests/middleware/test_wsgi.py
index fe527e373..316cb191f 100644
--- a/tests/middleware/test_wsgi.py
+++ b/tests/middleware/test_wsgi.py
@@ -92,7 +92,8 @@ def test_build_environ():
         "http_version": "1.1",
         "method": "GET",
         "scheme": "https",
-        "path": "/",
+        "path": "/sub/",
+        "root_path": "/sub",
         "query_string": b"a=123&b=456",
         "headers": [
             (b"host", b"www.example.org"),
@@ -117,7 +118,7 @@ def test_build_environ():
         "QUERY_STRING": "a=123&b=456",
         "REMOTE_ADDR": "134.56.78.4",
         "REQUEST_METHOD": "GET",
-        "SCRIPT_NAME": "",
+        "SCRIPT_NAME": "/sub",
         "SERVER_NAME": "www.example.org",
         "SERVER_PORT": 443,
         "SERVER_PROTOCOL": "HTTP/1.1",
diff --git a/tests/test_routing.py b/tests/test_routing.py
index cd6f37880..128f06674 100644
--- a/tests/test_routing.py
+++ b/tests/test_routing.py
@@ -1,5 +1,6 @@
 import contextlib
 import functools
+import json
 import typing
 import uuid
 
@@ -563,12 +564,12 @@ def test_url_for_with_root_path(test_client_factory):
     client = test_client_factory(
         app, base_url="https://www.example.org/", root_path="/sub_path"
     )
-    response = client.get("/")
+    response = client.get("/sub_path/")
     assert response.json() == {
         "index": "https://www.example.org/sub_path/",
         "submount": "https://www.example.org/sub_path/submount/",
     }
-    response = client.get("/submount/")
+    response = client.get("/sub_path/submount/")
     assert response.json() == {
         "index": "https://www.example.org/sub_path/",
         "submount": "https://www.example.org/sub_path/submount/",
@@ -1242,6 +1243,19 @@ async def echo_paths(request: Request, name: str):
     )
 
 
+async def pure_asgi_echo_paths(scope: Scope, receive: Receive, send: Send, name: str):
+    data = {"name": name, "path": scope["path"], "root_path": scope["root_path"]}
+    content = json.dumps(data).encode("utf-8")
+    await send(
+        {
+            "type": "http.response.start",
+            "status": 200,
+            "headers": [(b"content-type", b"application/json")],
+        }
+    )
+    await send({"type": "http.response.body", "body": content})
+
+
 echo_paths_routes = [
     Route(
         "/path",
@@ -1249,8 +1263,9 @@ async def echo_paths(request: Request, name: str):
         name="path",
         methods=["GET"],
     ),
+    Mount("/asgipath", app=functools.partial(pure_asgi_echo_paths, name="asgipath")),
     Mount(
-        "/root",
+        "/sub",
         name="mount",
         routes=[
             Route(
@@ -1258,7 +1273,7 @@ async def echo_paths(request: Request, name: str):
                 functools.partial(echo_paths, name="subpath"),
                 name="subpath",
                 methods=["GET"],
-            )
+            ),
         ],
     ),
 ]
@@ -1276,11 +1291,22 @@ def test_paths_with_root_path(test_client_factory: typing.Callable[..., TestClie
         "path": "/root/path",
         "root_path": "/root",
     }
+    response = client.get("/root/asgipath/")
+    assert response.status_code == 200
+    assert response.json() == {
+        "name": "asgipath",
+        "path": "/root/asgipath/",
+        # Things that mount other ASGI apps, like WSGIMiddleware, would not be aware
+        # of the prefixed path, and would have their own notion of their own paths,
+        # so they need to be able to rely on the root_path to know the location they
+        # are mounted on
+        "root_path": "/root/asgipath",
+    }
 
-    response = client.get("/root/root/path")
+    response = client.get("/root/sub/path")
     assert response.status_code == 200
     assert response.json() == {
         "name": "subpath",
-        "path": "/root/root/path",
-        "root_path": "/root",
+        "path": "/root/sub/path",
+        "root_path": "/root/sub",
     }