Abstract: Frequency hopping sequence is utilized to choose the frequency slot in frequency hopping communication. The theoretical bounds and sequence design are the primary research aspects of frequency hopping sequence. Based on the Hamming correlation and the partial Hamming correlation of frequency hopping sequences, we investigated the domestic and foreign research results of the theoretical bounds and sequence design of frequency hopping sequence. We also pointed out that the bounds and constructions of low hit zone frequency hopping sequence with optimal partial Hamming correlation are important trends for future development.