The problem of phase unwrapping in two dimensions has been studied extensively in the past two decades, but the three-dimensional (3D) problem has so far received relatively little attention. We develop here a theoretical framework for 3D phase unwrapping and also describe two algorithms for implementation, both of which can be applied to synthetic aperture radar interferometry (InSAR) time series. We test the algorithms on simulated data and find both give more accurate results than a two-dimensional algorithm. When applied to actual InSAR time series, we find good agreement both between the algorithms and with ground truth.