Data compression today is still as important as it was in the early days of computing. Although in those days all computer and storage resources were very limited, the objects in use were much smaller than today. We have seen a shift from generic compression to compression for specific file types, especially those in images, audio and video. In this weekend's back to basic reading we go back in time, 1987 to be specific, when Leweler and Hirschberg wrote a survey paper that covers the 40 years of data compression research. It covers all the areas that we like in a back to basics paper, it does not present the most modern results but it gives you a great understanding of the fundamentals. It is a substantial paper but easy to read.
Data compression, D.A. Lelewer and D.S. Hirschberg, Data compression, Computing Surveys 19,3 (1987) 261-297.