This synthesis lecture presents the current state-of-the-art in applying low-latency, lossless hardware compression algorithms to cache, memory, and the memory/cache link. There are many non-trivial challenges that must be addressed to make data compression work well in this context. First, since compressed data must be decompressed before it can be accessed, decompression latency ends up on the critical memory access path. This imposes a significant constraint on the choice of compression algorithms. Second, while conventional memory systems store fixed-size entities like data types, cache...