Quantitative phase microscopy (QPM) is a group of techniques that measure the optical path delays associated with a sample, which may be transparent, translucent or opaque. QPM systems can provide quantitative data about an object and have seen fast growing applications in a variety of fields including metrology, live cell imaging and multi-phase flow. In this disclosure, we describe novel QPM methods and a number of example apparatus. Based on special interferometry and signal processing, these methods can provide quantitative phase data of the sample at high speed (several hundred fps or higher) with very high sensitivity (well below 0.1nm). They are also free or nearly free of speckle noise, which causes significant degradation in system stability and sensitivity in many current QPM systems. These capabilities enable our methods to visualize sample features that are hard to detect, and quantify them in a dynamic fashion with unprecedented sensitivity.