Synthetic aperture radar is an important tool in a wide range of civilian and military imaging applications. This is primarily due to its ability to image in all weather conditions, during both the day and the night, unlike optical imaging systems. A synthetic aperture radar system contains a step which is not present in an optical imaging system, this is image formation. This is required because the acquired data from the radar sensor does not directly correspond to the image. Instead, to form an image, the system must solve an inverse problem. In conventional scenarios, this inverse problem is relatively straight forward and a matched lter based algorithm produces an image of suitable image quality. However, there are a number of interesting scenarios where this is not the case. Scenarios where standard image formation algorithms are unsuitable include systems with data undersampling, errors in the system observation model and data that is corrupted by radio frequency interference. Image formation in these scenarios will form the topics of this thesis and a number of iterative algorithms are proposed to achieve image formation. The motivation for these proposed algorithms is primarily from the eld of compressed sensing, which considers the recovery of signals with a low-dimensional structure. The rst contribution of this thesis is the development of fast algorithms for the system observation model and its adjoint. These algorithms are required by large-scale gradient based iterative algorithms for image formation. The proposed algorithms are based on existing fast back-projection algorithms, however, a new decimation strategy is proposed which is more suitable for some applications. The second contribution is the development of a framework for iterative near- eld image formation, which uses the proposed fast algorithms. It is shown that the framework can be used, in some scenarios, to improve the visual quality of images formed from fully sampled data and undersampled data, when compared to images formed using matched lter based algorithms. The third contribution concerns errors in the system observation model. Algorithms that correct these errors are commonly referred to as autofocus algorithms. It is shown that conventional autofocus algorithms, which work as a post-processor on the formed image, are unsuitable for undersampled data. Instead an autofocus algorithm is proposed which corrects errors within the iterative image formation procedure. The proposed algorithm is provably stable and convergent with a faster convergence rate than previous approaches. The nal contribution is an algorithm for ultra-wideband synthetic aperture radar image formation. Due to the large spectrum over which the ultra-wideband signal is transmitted, there is likely to be many other users operating within the same spectrum. These users can produce signi cant radio frequency interference which will corrupt the received data. The proposed algorithm uses knowledge of the RFI spectrum to minimise the e ect of the RFI on the formed image.