It is well known that data compression plays a significant role when using a modem connection for browsing web-pages on the Internet, reception of text files or large e-mail messages. Modem data compression is used most often for it, and the most popular compression protocol V.42bis serves exactly this purpose. A sending modem traces a data stream, and if data are compressible, it compresses them and then transfers them via a telephone network in a packed form. A receiving modem unpacks data and transfers them to a computer. Different data are compressed differently: modem compression allows for a gain from several percents to 5-10 times as compared with the initial volume. That is why it is important to know how good this function works in a certain modem. So, this review is aimed at comparison of effectiveness of different realization ways of compression protocols.