SRGM (software reliability and growth model), as an important mathematical tool of modeling reliability and improving reliability process, plays significant role in measuring, predicting and ensuring reliability, managing testing resources and releasing optimal software. Research on SRGM is elaborated and analyzed in this paper. First, main research content and modeling process of SRGM are analyzed, and the basic function is sketched. In the mean time, research evolution is summarized, the state of art is illustrated and the current research characteristics are formulated. Second, from the three aspects including the total number of faults in software, FDR (fault detection rate) and TE (testing-effort), the key factors influencing SRGM are analyzed. Based on the unified framework model proposed in author's previous research, the classical numerical models are classified, compared and analyzed. In addition, the SRGMs based on finite and infinite queue model are discussed and simulation technique emphasizing on RDEP (rate-driven event processes) is elaborated. Furthermore, to evaluate the differences in the models, 26 models are compared by 16 published failure data sets. Experimental results reveal that the differences depend on the objectivity of failure data set collected and the subjectivity of establishing mathematical model by researchers under the different assumptions. Finally, the challenges, the trend of development and the problems to be solved are pointed out.