As one novel lensless phase retrieval technique, ptychography greatly improves the convergence speed and the anti-noise capability of traditional phase iterative retrieval algorithms. Ptychography features a lot of merits, such as large field of view, high contrast, high resolution, and label-free as well as long working distance without losing low frequency phase component, which has been widely applied in various regions. The research status and the latest advances in the field of quantitative phase microscopy imaging are introduced, especially the fundamentals, technique advances and related applications of conventional ptychography (CP) and Fourier ptychography (FP). The fast FP and the fluorescence microscopy imaging based on FP are mainly discussed and the current problems and future trends of CP and FP are also summarized.