Algorithms and computational developments in recent years have yielded suitable techniques for overcoming the resolution limits imposed on conventional astronomical observations by atmospheric turbulence. The Knox-Thompson, triple-correlation, and phase-gradient algorithms are capable of reconstructing the diffraction-limited, complex spatial spectrum of an object from a sequence of short-exposure images. The basic principles of these techniques are reviewed with emphasis on photon-limited operation at visible wavelengths. Practical considerations, magnitude limits, and examples of recent applications are presented.