Remote sensing and surveillance are the main application areas for radar in general and synthetic aperture (SAR) radar in particular. Since the first radar system built by Hülsmeyer in 1904, radar has developed so that it is now able to create images from a large distance. In addition to this, the invention of synthetic aperture radar has enabled the ability to create images with high resolution. In this thesis, SAR systems capable of very high resolution imaging are considered, and data from such a system, namely CARABAS-II, is used. The higher the resolution of the system, the better the ability to extract information. The work presented in this thesis can be divided into two separate fields. The first and main area is speed estimation and the refocusing of moving targets in SAR imagery. The second area is related to SAR processing. In Part I of this thesis, a theoretical expression for the phase of a moving object in a SAR image is derived. Based on this expression, an estimator of relative speed is proposed. The estimator was tested in simulation and on CARABAS-II data, using a boat as a moving target. The results with regard to the focusing ability were satisfactory. In Part II, a comparison between two high resolution SAR processing algorithms, namely the polar and the subimage version of fast factorized back projection, is made. The comparison takes into account the difference in ability of obtaining very high quality images and gives a phase error analysis. In Part III, the effect of clutter statistics on the estimator is investigated. The sensitivity of the estimator to surrounding stationary targets (coherent clutter) and to thermal noise is examined. The results indicate that a target signal power of approximately 5dB above clutter (peak energy) or noise (average power) gives good results only using one iteration. Part IV is a continuation of Part I and III. In this part, a refocusing approach based on a SAR image is also developed and used. The central part of this refocusing approach is the derivation of a new refocusing equation. The results show that an image with many moving targets that have different normalized relative speeds can be focused.