Live video streaming is still a touchy subject and not well supported across browsers and mobile devices. Hence I did a short overview of how to start on this years WebCamp Ljubljana. The lecture has since been published as a video as well.
Relevant links from the slides:
Pre-built FFMpeg downloads - Official FFMpeg site with precompiled ffmpeg builds for major platforms
Nginx RTMP module - Video streaming server module for Nginx with RTMP, (Apple) HLS and DASH support
Video.js HTML5 video player - Free HTML5 video player that automatically detects browser capabilities and switches to Flash when necessary
Media sources and HLS modules for Video.js player required for HLS live streaming support
The lecture video and slides: