Optical microscopy has been a commonly used method of investigation in medicine and biology. Numerous biological samples, including live cells, are quite transparent under visible light illumination and behave essentially as phase objects. Techniques such as phase contrast and Nomarski microscopy provide contrast of nearly invisible samples by transforming the phase information into intensity distribution and thus reveal structural details of biological systems. However, the information obtained with these techniques about the phase shift associated with the illuminating field is only qualitative. Retrieving quantitative phase information from transparent objects with high accuracy and low noise allows for measurements in the biological investigation of structure and dynamics. Both interferometric and non-interferometric techniques have been proposed for quantitative phase imaging of biological samples. Also Fourier phase microscopy (FPM) has been developed as an extremely low-noise phase imaging method. Due to the sub-nanometer phase stability over extended periods of time, FPM is suitable for investigating dynamics in biological systems on time scales from seconds to a cell lifetime.