Large field of view, high resolution, and phase imaging are long-term goals pursued in the field of optical microscopy. Nevertheless, it is difficult to balance these performances in the conventional optical microscopic framework, which largely limits the application scope of conventional optical microscopy. Conventional microscopic imaging methods improve the imaging space-bandwidth product (SBP) or phase-imaging capability at the expense of a significant increase in the system construction cost or decrease in other imaging performances. Fourier ptychographic microscopy (FPM), as a representative computational microscopy imaging technology framework, can achieve large SBP and quantitative phase imaging simultaneously, without requiring precision mechanical scanning devices and interferometric systems. FPM has been widely studied and used in the fields of digital microscopy and life sciences; it has high research value and application prospects. In this article, the related research progress of FPM from the aspects of basic physical model, phase-recovery algorithm, and system-construction method is reviewed. In addition, the theory and application development direction of FPM are analyzed and discussed.