Digital holography has received recent attention for many imaging and sensing applications, including imaging through turbulent and turbid media, adaptive optics, three-dimensional projective display technology and optical tweezing. It holds several advantages over classical methods for wavefront sensing and adaptive-optics correction, chief among these being significantly fewer and simpler optical components. A significant obstacle for digital holography in real-time applications, such as wavefront sensing for high-energy laser systems and high-speed imaging for target tracking, is the fact that digital holography is computationally intensive; it requires iterative virtual wavefront propagation and hill-climbing algorithms to optimize sharpness criteria. This research demonstrates real-time methods for digital holography based on approaches for optimal and adaptive identification, prediction, and control of optical wavefronts. The methods presented integrate minimum-variance wavefront prediction into dynamic digital holography schemes to accelerate the wavefront correction and image sharpening algorithms. Further gains in computational efficiency are demonstrated in this work with a variant of localized sharpening in conjunction with predictive dynamic digital holography for real-time applications. This "subspace correction" method optimizes sharpness of local regions in a detector plane by parallel independent wavefront correction on reduced-dimension subspaces of the complex field in a spectral plane.ii The dissertation of Sennan David Sulaiman is approved.