This chapter provides background about Hybrid Automatic Repeat reQuest (HARQ) protocols. First, the critical situations that may be faced by wireless communication systems especially cellular mobile technologies in case of very noisy radio channels are introduced. Particularly, the chapter introduces the HARQ protocols, their main constituent components as well as some related application areas. Then, the state-of-the-art of HARQ protocols is presented. The next section explains the three basic ARQ protocols. Then, the different HARQ types are detailed. Then, a mathematical model of type II HARQ based on Rayleigh fading channel is provided. This analytical analysis is followed by a discussion of the throughput which is one of the most interesting metrics used to measure the performance of HARQ systems. The readers can find in the next section a description of the HARQ systems architecture where 3GPP LTE is used to illustrate and explain how such systems operate. Finally, the last section concludes the chapter.