Compression Basics
I had contemplated authoring an article about compression, but came across an interesting series of articles from DSP DesignLine.
Here is an excellent background tutorial on data compression written by Steven W. Smith, Ph.D.:
Data Compression: Part 1 (Huffman and RLE explored)
Data Compression: Part 2 (Delta encoding and GIF explored)
Data Compression: Part 3 (JPEG and MPEG explored)
Video Compression (a much older article written by Amit Shoham, but good nonetheless)