diff --git a/README.md b/README.md
index 94110087..4e06793e 100644
--- a/README.md
+++ b/README.md
@@ -2,7 +2,7 @@
 <img width="400px" src="https://raw.githubusercontent.com/FluxML/fluxml.github.io/master/logo.png"/>
 </p>
 
-[![Build Status](https://travis-ci.org/FluxML/Flux.jl.svg?branch=master)](https://travis-ci.org/FluxML/Flux.jl) [![](https://img.shields.io/badge/docs-stable-blue.svg)](https://fluxml.github.io/Flux.jl/stable/) [![](https://img.shields.io/badge/chat-on%20slack-yellow.svg)](https://slackinvite.julialang.org/) [![DOI](http://joss.theoj.org/papers/10.21105/joss.00602/status.svg)](https://doi.org/10.21105/joss.00602)
+[![Build Status](https://travis-ci.org/FluxML/Flux.jl.svg?branch=master)](https://travis-ci.org/FluxML/Flux.jl) [![](https://img.shields.io/badge/docs-stable-blue.svg)](https://fluxml.github.io/Flux.jl/stable/) [![](https://img.shields.io/badge/chat-on%20slack-yellow.svg)](https://slackinvite.julialang.org/) [![DOI](https://joss.theoj.org/papers/10.21105/joss.00602/status.svg)](https://doi.org/10.21105/joss.00602)
 
 Flux is an elegant approach to machine learning. It's a 100% pure-Julia stack, and provides lightweight abstractions on top of Julia's native GPU and AD support. Flux makes the easy things easy while remaining fully hackable.
 
@@ -10,7 +10,7 @@ Flux is an elegant approach to machine learning. It's a 100% pure-Julia stack, a
 julia> Pkg.add("Flux")
 ```
 
-See the [documentation](http://fluxml.github.io/Flux.jl/) or the [model zoo](https://github.com/FluxML/model-zoo/) for examples.
+See the [documentation](https://fluxml.github.io/Flux.jl/) or the [model zoo](https://github.com/FluxML/model-zoo/) for examples.
 
 If you use Flux in research, please cite the following paper:
 
diff --git a/paper/paper.bib b/paper/paper.bib
index c8e6dbd5..d1e2995a 100644
--- a/paper/paper.bib
+++ b/paper/paper.bib
@@ -14,7 +14,7 @@
   journal   = {arXiv},
   volume    = {abs/11712.03112},
   year      = {2017},
-  url       = {http://arxiv.org/abs/1712.03112},
+  url       = {https://arxiv.org/abs/1712.03112},
 }
 
 @online{MLPL,
@@ -29,7 +29,7 @@
   author = {Mike Innes and others},
   title = {Generic GPU Kernels},
   year = 2017,
-  url = {http://mikeinnes.github.io/2017/08/24/cudanative.html},
+  url = {https://mikeinnes.github.io/2017/08/24/cudanative.html},
   urldate = {2018-02-16}
 }
 
diff --git a/src/data/cmudict.jl b/src/data/cmudict.jl
index f89ded4f..e6266540 100644
--- a/src/data/cmudict.jl
+++ b/src/data/cmudict.jl
@@ -19,7 +19,7 @@ function load()
   @info "Downloading CMUDict dataset"
   mkpath(deps("cmudict"))
   for (x, hash) in suffixes_and_hashes
-    download_and_verify("$cache_prefix/http://svn.code.sf.net/p/cmusphinx/code/trunk/cmudict/cmudict-$version$x",
+    download_and_verify("$cache_prefix/https://svn.code.sf.net/p/cmusphinx/code/trunk/cmudict/cmudict-$version$x",
              deps("cmudict", "cmudict$x"), hash)
   end
 end
diff --git a/src/data/iris.jl b/src/data/iris.jl
index 789ea696..3da90330 100644
--- a/src/data/iris.jl
+++ b/src/data/iris.jl
@@ -26,7 +26,7 @@ function load()
     isfile(deps("iris.data")) && return
 
     @info "Downloading iris dataset."
-    download_and_verify("$(cache_prefix)http://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data",
+    download_and_verify("$(cache_prefix)https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data",
                         deps("iris.data"),
                         "6f608b71a7317216319b4d27b4d9bc84e6abd734eda7872b71a458569e2656c0")
 end
diff --git a/src/layers/recurrent.jl b/src/layers/recurrent.jl
index 4e23e9ee..61bbec4e 100644
--- a/src/layers/recurrent.jl
+++ b/src/layers/recurrent.jl
@@ -153,7 +153,7 @@ Base.show(io::IO, l::LSTMCell) =
 Long Short Term Memory recurrent layer. Behaves like an RNN but generally
 exhibits a longer memory span over sequences.
 
-See [this article](http://colah.github.io/posts/2015-08-Understanding-LSTMs/)
+See [this article](https://colah.github.io/posts/2015-08-Understanding-LSTMs/)
 for a good overview of the internals.
 """
 LSTM(a...; ka...) = Recur(LSTMCell(a...; ka...))
@@ -194,7 +194,7 @@ Base.show(io::IO, l::GRUCell) =
 Gated Recurrent Unit layer. Behaves like an RNN but generally
 exhibits a longer memory span over sequences.
 
-See [this article](http://colah.github.io/posts/2015-08-Understanding-LSTMs/)
+See [this article](https://colah.github.io/posts/2015-08-Understanding-LSTMs/)
 for a good overview of the internals.
 """
 GRU(a...; ka...) = Recur(GRUCell(a...; ka...))
diff --git a/src/optimise/optimisers.jl b/src/optimise/optimisers.jl
index 40b8fd33..ec7c8aa6 100644
--- a/src/optimise/optimisers.jl
+++ b/src/optimise/optimisers.jl
@@ -66,7 +66,7 @@ end
 """
     RMSProp(η = 0.001, ρ = 0.9)
 
-[RMSProp](http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf)
+[RMSProp](https://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf)
 optimiser. Parameters other than learning rate don't need tuning. Often a good
 choice for recurrent networks.
 """
@@ -155,7 +155,7 @@ end
 """
     ADADelta(ρ = 0.9, ϵ = 1e-8)
 
-[ADADelta](http://arxiv.org/abs/1212.5701) optimiser. Parameters don't need
+[ADADelta](https://arxiv.org/abs/1212.5701) optimiser. Parameters don't need
 tuning.
 """
 mutable struct ADADelta