With the growing importance of single-photon-counting (SPC) techniques, researchers are now designing high-performance systems based on single-photon avalanche diodes (SPADs). SPADs with high performances and low cost allow the popularity of SPC-based systems for medical and industrial applications. However, few efforts were put into the design optimization of SPADs due to limited calibrated models of the SPAD itself and its related circuits. This paper provides a perspective on improving SPAD-based system design by reviewing the development of SPAD models. First, important SPAD principles such as photon detection probability (PDP), dark count rate (DCR), afterpulsing probability (AP), and timing jitter (TJ) are discussed. Then a comprehensive discussion of various SPAD models focusing on each of the parameters is provided. Finally, important research challenges regarding the development of more advanced SPAD models are summarized, followed by the outlook for the future development of SPAD models and emerging SPAD modeling methods.