Bump minimum Rust version to 1.37.0

diff --git a/.travis.yml b/.travis.yml
index 107ba81..8116ed7 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -16,7 +16,7 @@
   - osx
 
 rust:
-  - 1.36.0
+  - 1.37.0
   - stable
   - nightly
 
@@ -43,9 +43,9 @@
       os: linux
       env: RUSTFMT=true
       rust: nightly
-    - name: "Windows 1.36.0"
+    - name: "Windows 1.37.0"
       os: windows
-      rust: 1.36.0-x86_64-pc-windows-msvc
+      rust: 1.37.0-x86_64-pc-windows-msvc
     - name: "Windows Stable"
       os: windows
       rust: stable-x86_64-pc-windows-msvc
diff --git a/CHANGELOG.md b/CHANGELOG.md
index 4f47f4f..0598fed 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -6,6 +6,10 @@
 
 ## 0.4.2-dev
 
+### Packaging
+
+- Minimum Rust version has been bumped to 1.37.0
+
 ### Changed
 
 - Pressing additional modifiers for mouse bindings will no longer trigger them
diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
index 9778252..7b97743 100644
--- a/CONTRIBUTING.md
+++ b/CONTRIBUTING.md
@@ -42,7 +42,7 @@
 [easy](https://github.com/alacritty/alacritty/issues?q=is%3Aopen+is%3Aissue+label%3A%22D+-+easy%22)
 issues.
 
-Please note that the minimum supported version of Alacritty is Rust 1.36.0. All patches are expected
+Please note that the minimum supported version of Alacritty is Rust 1.37.0. All patches are expected
 to work with the minimum supported version.
 
 ### Testing
diff --git a/extra/linux/redhat/alacritty.spec b/extra/linux/redhat/alacritty.spec
index a253c67..c098309 100644
--- a/extra/linux/redhat/alacritty.spec
+++ b/extra/linux/redhat/alacritty.spec
@@ -7,7 +7,7 @@
 VCS:           https://github.com/alacritty/alacritty.git
 Source:        alacritty-%{version}.tar
 
-BuildRequires: rust >= 1.36.0
+BuildRequires: rust >= 1.37.0
 BuildRequires: cargo
 BuildRequires: cmake
 BuildRequires: freetype-devel