diff --git a/news/1 Enhancements/5047.md b/news/1 Enhancements/5047.md
new file mode 100644
index 000000000000..db9fb682e4af
--- /dev/null
+++ b/news/1 Enhancements/5047.md	
@@ -0,0 +1 @@
+Support running under docker.
diff --git a/package.json b/package.json
index 78aaebb0fe17..a18b66a42343 100644
--- a/package.json
+++ b/package.json
@@ -2398,8 +2398,8 @@
         "mocha-junit-reporter": "^1.17.0",
         "mocha-multi-reporters": "^1.1.7",
         "node-has-native-dependencies": "^1.0.2",
-        "node-sass": "^4.11.0",
         "node-html-parser": "^1.1.13",
+        "node-sass": "^4.11.0",
         "nyc": "^13.3.0",
         "raw-loader": "^0.5.1",
         "react": "^16.5.2",
diff --git a/src/client/datascience/constants.ts b/src/client/datascience/constants.ts
index d128e70ca7f9..17a8809dc291 100644
--- a/src/client/datascience/constants.ts
+++ b/src/client/datascience/constants.ts
@@ -48,7 +48,15 @@ export namespace RegExpValues {
     export const CheckJupyterRegEx = IS_WINDOWS ? /^jupyter?\.exe$/ : /^jupyter?$/;
     export const PyKernelOutputRegEx = /.*\s+(.+)$/m;
     export const KernelSpecOutputRegEx = /^\s*(\S+)\s+(\S+)$/;
-    export const UrlPatternRegEx = /(https?:\/\/[^\s]+)/ ;
+    // This next one has to be a string because uglifyJS isn't handling the groups. We use named-js-regexp to parse it
+    // instead.
+    export const UrlPatternRegEx = '(?<PREFIX>https?:\\/\\/)((\\(.+\\s+or\\s+(?<IP>.+)\\))|(?<LOCAL>[^\\s]+))(?<REST>:.+)' ;
+    export interface IUrlPatternGroupType {
+        LOCAL: string | undefined;
+        PREFIX: string | undefined;
+        REST: string | undefined;
+        IP: string | undefined;
+    }
     export const HttpPattern = /https?:\/\//;
     export const ExtractPortRegex = /https?:\/\/[^\s]+:(\d+)[^\s]+/;
     export const ConvertToRemoteUri = /(https?:\/\/)([^\s])+(:\d+[^\s]*)/;
diff --git a/src/client/datascience/jupyter/jupyterConnection.ts b/src/client/datascience/jupyter/jupyterConnection.ts
index 0d8bd098abde..149f48f62719 100644
--- a/src/client/datascience/jupyter/jupyterConnection.ts
+++ b/src/client/datascience/jupyter/jupyterConnection.ts
@@ -18,6 +18,10 @@ import { RegExpValues } from '../constants';
 import { IConnection } from '../types';
 import { JupyterConnectError } from './jupyterConnectError';
 
+// tslint:disable-next-line:no-require-imports no-var-requires no-any
+const namedRegexp = require('named-js-regexp');
+const urlMatcher = namedRegexp(RegExpValues.UrlPatternRegEx);
+
 export type JupyterServerInfo = {
     base_url: string;
     notebook_dir: string;
@@ -130,14 +134,19 @@ class JupyterConnectionWaiter {
 
     // tslint:disable-next-line:no-any
     private getJupyterURLFromString(data: any) {
-        const urlMatch = RegExpValues.UrlPatternRegEx.exec(data);
-        if (urlMatch && !this.startPromise.completed) {
+        const urlMatch = urlMatcher.exec(data) as any;
+        const groups = urlMatch.groups() as RegExpValues.IUrlPatternGroupType;
+        if (urlMatch && !this.startPromise.completed && groups && (groups.LOCAL || groups.IP)) {
+            // Rebuild the URI from our group hits
+            const host = groups.LOCAL ? groups.LOCAL : groups.IP;
+            const uriString = `${groups.PREFIX}${host}${groups.REST}`;
+
             // URL is not being found for some reason. Pull it in forcefully
             // tslint:disable-next-line:no-require-imports
             const URL = require('url').URL;
             let url: URL;
             try {
-                url = new URL(urlMatch[0]);
+                url = new URL(uriString);
             } catch (err) {
                 // Failed to parse the url either via server infos or the string
                 this.rejectStartPromise(localize.DataScience.jupyterLaunchNoURL());
diff --git a/src/client/datascience/jupyter/jupyterExecution.ts b/src/client/datascience/jupyter/jupyterExecution.ts
index 0eec7c30a096..ceeaa54dc43f 100644
--- a/src/client/datascience/jupyter/jupyterExecution.ts
+++ b/src/client/datascience/jupyter/jupyterExecution.ts
@@ -36,6 +36,7 @@ import {
 import { JupyterConnection, JupyterServerInfo } from './jupyterConnection';
 import { JupyterKernelSpec } from './jupyterKernelSpec';
 import { JupyterWaitForIdleError } from './jupyterWaitForIdleError';
+import { execSync } from 'child_process';
 
 enum ModuleExistsResult {
     NotFound,
@@ -351,6 +352,26 @@ export class JupyterExecutionBase implements IJupyterExecution {
                 extraArgs.push('--debug');
             }
 
+            // Check for a docker situation.
+            try {
+                if (await this.fileSystem.fileExists('/proc/self/cgroup')) {
+                    const cgroup = await this.fileSystem.readFile('/proc/self/cgroup');
+                    if (cgroup.includes('docker')) {
+                        // We definitely need an ip address.
+                        extraArgs.push('--ip');
+                        extraArgs.push('127.0.0.1');
+    
+                        // Now see if we need --allow-root.
+                        const idResults = execSync('id', {encoding: 'utf-8'});
+                        if (idResults.includes('(root)')) {
+                            extraArgs.push('--allow-root');
+                        }
+                    }
+                }
+            } catch {
+                noop();
+            }
+
             // Use this temp file and config file to generate a list of args for our command
             const args: string[] = [...['--no-browser', `--notebook-dir=${tempDir.path}`], ...extraArgs];