Computational imaging involves the joint design of imaging system hardware and software, optimizing across the entire pipeline from acquisition to reconstruction. Computers can replace bulky and expensive optics by solving computational inverse problems. This talk will describe new microscopes that use computational imaging to enable 3D, super-resolution and phase imaging with simple and inexpensive hardware. Our reconstruction algorithms are based on large-scale nonlinear non-convex optimization. Applications span optical bioimaging, X-ray lithography and atomic-resolution electron microscopy.