Over the past few decades, frequency hopping (FH) techniques have attracted considerable interest in both military and commercial communications. However, fading and interference can significantly degrade the performance of an FH system. One method commonly employed to overcome the degradation in performance because of the fading is the use of diversity. Furthermore, fast FH (FFH) systems can enjoy both time and frequency diversity and hence FFH systems employed in conjunction with diversity-combining techniques are effective for combating fading and interference effects. In this study, the authors provide a comprehensive survey on the past and current research work on diversity-combining techniques for suppressing different types of interference in FFH M-ary frequency-shiftkeying systems over various fading channels. Some commonly used theoretical approaches for analysing performance of FFH systems are also presented. In addition to the survey, they will also discuss some interesting areas of future work in this research topic.