LZ77 and LZ78
Today, there are many variations of these algorithms. Examples of  such variations are  LZW, LZSS, or LZMA. Lempel-Ziv-Welch (LZW) is a variant that was published in 1983, and that was used for the GIF format used by Compuserve, or the  the DEFLATE algorithm used in PNG and ZIP.