Conventional microwave and futuristic optical radar imaging requires estimating a function from limited Fourier information and a priori constraints. Linear problems include estimation from complex Fourier samples that are irregularly spaced on a polar grid (spotlight SAR), on a sinusoidal grid (laser SAR), or on a random grid (anti-aliasing phased array). Nonlinear problems include the famous phase retrieval problem of estimating a two-dimensional band limited function from its approximate Fourier modulus over a spatial region. Several deterministic and iterative methods for linear problems are described and their algorithmic complexity is discussed. A new method for attacking the infamous 'stagnation' problem that characterizes iterative methods for the phase retrieval problem is described. The method, which originated from consideration of spin-glass models of statistical lattice physics, incorporates partial information about the zero-set of the analytic continuation of the squared Fourier transform modulus in order to break the 'twin-object' symmetry responsible for stagnation.