This paper employs adaptive filtering and control for reconstruction and prediction of wavefronts and for control of laser beam jitter in an adaptive optics system. Adaptive compensation is needed in many adaptive optics applications because wind velocities and the strength of atmospheric-turbulence can change rapidly, rendering any fixed-gain reconstruction algorithm far from optimal. Also, vibration of the optical platform commonly produces laser beam jitter. The performance of the methods proposed here is illustrated by application to recently developed simulations of high energy laser propagation through extended turbulence.