The quantitative phase microscopy is sensitive to environmental disturbance. It has been a hot topic that how to get rid of the influence of environmental disturbance on quantitative phase imaging. This review focuses on the common-path digital holography microscopy (DHM) and single beam quantitative phase microscopy. The former mainly includes Fizeau interference microscopy, Mirau interference microscopy, off-axis and coaxial point diffraction interference microscopy, DHM of double spherical illumination, and spatially-multiplexed DHM. The latter mainly includes coaxial digital holography, and quantitative phase-contrast microscopy based on parallel light illumination, ultra-oblique illumination, and multi-point off-axis illumination. We hope that this review will provide useful reference for the construction of high stability and practical quantitative phase microscopic devices.