Fourier ptychographic microscopy(FPM) is a promising label-free computational imaging technique with high resolution, wide field-of-view(FOV) and quantitative phase recovery. Due to its flexible setup, promising high-contrast performance without mechanical scanning and interferometric measurements, FPM has wide applications in the digital pathology, observation and dynamic imaging of label-free cells in vitro. In this review, the principle, research status and the latest advances were introduced in several aspects of FPM such as the system calibration methods, high-throughput imaging and high-speed imaging. The current problems and future trends were also presented.