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Most living cells do not absorb or scatter light significantly, i.e. they are essentially transparent, or phase objects. Phase contrast microscopy proposed by Zernike in the 1930’s represents a major advance in intrinsic contrast imaging, as it reveals inner details of transparent structures without staining or tagging. While phase contrast is sensitive to optical path-length changes in the cell, the information retrieved is only qualitative. Quantifying cell-induced optical pathlength shifts permits nanometer scale measurements of structures and motions in a non-contact, non-invasive manner. Furthermore, the phase information allows for retrieving tomography of transparent structures such as cells. This is an inverse problem analog to that in X-ray diffraction applications (e.g., crystallography), where the phase signal is not readily available. Thus, quantitative phase imaging (QPI) has recently become an active field of study, with applications in both materials and life sciences. We have developed Diffraction phase microscopy (DPM) and Spatial Light Interference Microscopy (SLIM) as two complementary methods for QPI. They share the idea of common-path interferometry, which adds stability to the phase measurements. I will review several applications of this method in basic science and clinical diagnosis. I will end with a discussion of recent results using QPI for pump-probe applications of nonlinear laser-matter interactions.