diff --git a/package.json b/package.json
index 6c40a97175..88d4ac89d1 100644
--- a/package.json
+++ b/package.json
@@ -46,7 +46,7 @@
     "to-markdown": "3.1.0",
     "ts-loader": "5.3.3",
     "ts-node": "7.0.1",
-    "typescript": "3.3.1",
+    "typescript": "3.5.1",
     "underscore": "1.9.1",
     "webfonts-generator": "0.4.0",
     "webpack": "4.32.2",
diff --git a/static/js/tsconfig.json b/static/js/tsconfig.json
index 79e465ddf6..442398e616 100644
--- a/static/js/tsconfig.json
+++ b/static/js/tsconfig.json
@@ -1,5 +1,11 @@
 {
     "compilerOptions": {
+        /* Typescript 3.4 added the --incremental flag but its API is not
+         * currently public so ts-loader cannot use it yet.
+         * Tracking issue: https://github.com/microsoft/TypeScript/issues/29978
+         */
+        // "incremental": true,
+
         /* Basic options */
         "target": "es5",
         "module": "es6",
diff --git a/tools/webpack.config.ts b/tools/webpack.config.ts
index b310bc1728..234539f6db 100644
--- a/tools/webpack.config.ts
+++ b/tools/webpack.config.ts
@@ -1,6 +1,9 @@
 import { resolve } from 'path';
 import * as BundleTracker from 'webpack-bundle-tracker';
 import * as webpack from 'webpack';
+// The devServer member of webpack.Configuration is managed by the
+// webpack-dev-server package. We are only importing the type here.
+import * as _webpackDevServer from 'webpack-dev-server';
 import { getExposeLoaders, getImportLoaders } from './webpack-helpers';
 import * as MiniCssExtractPlugin from 'mini-css-extract-plugin';
 
diff --git a/yarn.lock b/yarn.lock
index 0b124b32de..dfdffb8e45 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -11285,10 +11285,10 @@ typedarray@^0.0.6:
   resolved "https://registry.yarnpkg.com/typedarray/-/typedarray-0.0.6.tgz#867ac74e3864187b1d3d47d996a78ec5c8830777"
   integrity sha1-hnrHTjhkGHsdPUfZlqeOxciDB3c=
 
-typescript@3.3.1:
-  version "3.3.1"
-  resolved "https://registry.yarnpkg.com/typescript/-/typescript-3.3.1.tgz#6de14e1db4b8a006ac535e482c8ba018c55f750b"
-  integrity sha512-cTmIDFW7O0IHbn1DPYjkiebHxwtCMU+eTy30ZtJNBPF9j2O1ITu5XH2YnBeVRKWHqF+3JQwWJv0Q0aUgX8W7IA==
+typescript@3.5.1:
+  version "3.5.1"
+  resolved "https://registry.yarnpkg.com/typescript/-/typescript-3.5.1.tgz#ba72a6a600b2158139c5dd8850f700e231464202"
+  integrity sha512-64HkdiRv1yYZsSe4xC1WVgamNigVYjlssIoaH2HcZF0+ijsk5YK2g0G34w9wJkze8+5ow4STd22AynfO6ZYYLw==
 
 uglify-js@^2.6, uglify-js@^2.6.0:
   version "2.8.29"