Structured illumination microscopy (SIM) has become one of the most popular super-resolution (SR) instruments for dynamic imaging of live cells. However, the final SR images of SIM depends heavily on the image reconstruction algorithms, which could dramatically affect the image quality. In the past five years, nearly 10 open-source software packages for SIM reconstruction have been developed with advantage on different situations. And deep learning based SIM reconstruction algorithms has also been reported. Understanding the principles and differences of each algorithm becomes a priority to select the appropriate algorithms for practical applications. This review firstly introduces the principle of SIM, and then presents the latest advances for the reference of SIM researchers and users from three aspects: estimation of structured illumination parameter, spectrum optimization, and deep learning based reconstruction. Finally, the remaining issues that need to be addressed further for high-quality SIM super-resolution image reconstruction are summarized.