Where do the other popular compression utilities (e.g. bzip2, xzip, lzma, 7zip) fit in to this?
Run Length Encoding
Huffman Encoding
Lempel Ziv (LZ77)
Burrows Wheeler Transform
The interesting part of all these specific implementations is their own specialized way of extending or combining these algorithms for their own niche (or tradeoff point).
Bzip2 is for example, compresses really well because BWT is expensive, but clever - rzip extends the LZ part of bzip2 to look further across the file (instead of a few hundred kb).
Zlib itself has enough of these flags exposed out, so all Zlib isn't really the same - Z_FILTERED, Z_HUFFMAN_ONLY, Z_FIXED, Z_RLE etc. Look at something like Zopfli to see how they can be remixed, provided the tradeoffs of CPU change from the historic positions of Zlib.