Neural Art

Recently there have been big advancements in image classification due to architectural improvements such as convolutions and inceptions, partially inspired by biological networks.
Reverse-engineering these networks not only gives a glimpse into the inner workings of these algorithms, but also suggests intriguing parallels between machine and human perception and offers artists new techniques for digital image creation.
For example:
Deepdream
Neural Style

Other applications of deep learning:
Chatbots
Language Translation

Several libraries have been developed to ease the task of building neural networks, including:

Caffe
How to install Caffe on Mac OS X 10.11
Install caffe on Mac with El Capitan
Tensorflow