Quantitative phase imaging (QPI) utilizes the fact that the phase of an imaging field is much more sensitive than its amplitude. As fields from the source interact with the specimen, local variations in the phase front are produced, which provide structural information about the sample and can be used to reconstruct its topography with nanometer accuracy. QPI techniques do not require staining or coating of the specimen and are therefore nondestructive. Diffraction phase microscopy (DPM) combines many of the best attributes of current QPI methods; its compact configuration uses a common-path off-axis geometry which realizes the benefits of both low noise and single-shot imaging. This unique collection of features enables the DPM system to monitor, at the nanoscale, a wide variety of phenomena in their natural environments. Over the past decade, QPI techniques have become ubiquitous in biological studies and a recent effort has been made to extend QPI to materials science applications. We briefly review several recent studies which include real-time monitoring of wet etching, photochemical etching, surface wetting and evaporation, dissolution of biodegradable electronic materials, and the expansion and deformation of thin-films. We also discuss recent advances in semiconductor wafer defect detection using QPI.