This thesis describes the application of the Cramér Rao inequality to synthetic aperture radar (SAR). The resulting Cramér Rao lower bounds (CRB) reveal the smallest possible error variances for target parameter estimates (position and reflectivity), regardless of the estimator or SAR processing. The performance bounds are consequently used to design synthetic arrays and evaluate multistatic SAR configurations. We show that optimal sensor arrangements of synthetic arrays offer the possibility for single-pass, monostatic SAR to mitigate an effect known as layover that often distorts radar imagery. We also show these nonlinear apertures can be used to image targets in three dimensions. Furthermore, a new detection/estimation algorithm for targets in SAR imagery is developed and mean-squared errors from Monte Carlo simulations are compared to corresponding CRBs. Finally, a dynamic model-based estimation algorithm is developed for SAR to localize targets behind building walls. This iterative, optimization technique shows the potential to avert the combinatorial complexity and local maximization associated with many classification problems requiring model-based solutions.