diff --git a/build/docker/README.md b/build/docker/README.md
index 6f9c024..6f170e1 100644
--- a/build/docker/README.md
+++ b/build/docker/README.md
@@ -194,4 +194,4 @@
 | ruby      | 2.3.1p112     | 2.5.1p57      |       |
 | rust      | 1.34.0        | 1.35.0        |       |
 | smalltalk |               |               | Not in CI |
-| swift     |               | 4.2.1         |       |
+| swift     |               | 5.1.4         |       |
diff --git a/build/docker/ubuntu-bionic/Dockerfile b/build/docker/ubuntu-bionic/Dockerfile
index 464af0b..c22a859 100644
--- a/build/docker/ubuntu-bionic/Dockerfile
+++ b/build/docker/ubuntu-bionic/Dockerfile
@@ -247,14 +247,14 @@
       ruby-bundler
 
 # Rust dependencies
-RUN curl https://sh.rustup.rs -sSf | sh -s -- --default-toolchain 1.35.0 -y
+RUN curl https://sh.rustup.rs -sSf | sh -s -- --default-toolchain 1.36.0 -y
 ENV PATH /root/.cargo/bin:$PATH
 
 # Swift on Linux for cross tests
 RUN cd / && \
-    wget --quiet https://swift.org/builds/swift-4.2.1-release/ubuntu1804/swift-4.2.1-RELEASE/swift-4.2.1-RELEASE-ubuntu18.04.tar.gz && \
-    tar xf swift-4.2.1-RELEASE-ubuntu18.04.tar.gz --strip-components=1 && \
-    rm swift-4.2.1-RELEASE-ubuntu18.04.tar.gz && \
+    wget --quiet https://swift.org/builds/swift-5.1.4-release/ubuntu1804/swift-5.1.4-RELEASE/swift-5.1.4-RELEASE-ubuntu18.04.tar.gz && \
+    tar xf swift-5.1.4-RELEASE-ubuntu18.04.tar.gz --strip-components=1 && \
+    rm swift-5.1.4-RELEASE-ubuntu18.04.tar.gz && \
     swift --version
 
 # cppcheck-1.82 has a nasty cpp parser bug, so we're using something newer
diff --git a/lib/swift/Sources/THTTPSessionTransport.swift b/lib/swift/Sources/THTTPSessionTransport.swift
index 3c0af8e..f66da92 100644
--- a/lib/swift/Sources/THTTPSessionTransport.swift
+++ b/lib/swift/Sources/THTTPSessionTransport.swift
@@ -18,8 +18,15 @@
 */
 
 import Foundation
-import Dispatch
 
+// Conditional import for URLRequest
+// It was moved from Foundation to FoundationNetworking in 5.1, but
+// not on Darwin. See  https://stackoverflow.com/a/58606520
+#if canImport(FoundationNetworking)
+import FoundationNetworking
+#endif
+
+import Dispatch
 
 public class THTTPSessionTransport: TAsyncTransport {
   public class Factory : TAsyncTransportFactory {