The physical nature of time variable objects is often inferred from photometric light-curves and spectroscopic variations. Long-baseline optical interferometry has the power to resolve the spatial structure of time variable sources directly in order to measure their physical properties and test the physics of the underlying models. Recent interferometric studies of variable objects include measuring the angular expansion and spatial structure during the early stages of novae outbursts, studying the transits and tidal distortions of the components in eclipsing and interacting binaries, measuring the radial pulsations in Cepheid variables, monitoring changes in the circumstellar discs around rapidly rotating massive stars, and imaging starspots. Future applications include measuring the image size and centroid displacements in gravitational microlensing events, and imaging the transits of exoplanets. Ongoing and upcoming photometric surveys will dramatically increase the number of time-variable objects detected each year, providing many potential targets to observe interferometrically. For short-lived transient events, it is critical for interferometric arrays to have the flexibility to respond rapidly to targets of opportunity and optimize the selection of baselines and beam combiners to provide the necessary resolution and sensitivity to resolve the source as its brightness and size change. We discuss the science opportunities made possible by resolving variable sources using long baseline optical interferometry.