Phase contrast microscopy allows viewing of unstained living cells by converting phase changes in light passing through the sample into brightness changes in the image. It works by using an annular diaphragm to illuminate the sample with a ring of light and a phase plate to introduce additional phase shifts. Areas of different refractive index appear brighter or darker, creating contrast without requiring staining. Phase contrast microscopy is widely used for biological studies as it enables observation of cellular structures and dynamic processes in living cells over time.