A number of new techniques for solving multi-dimensional phase problems and blind deconvolution problems are presented. Some of these techniques augment existing algorithms, while others constitute original algorithms. The phase problem and blind deconvolution problem are reviewed. A comprehensive description of existing methods for effecting phase retrieval and blind deconvolution is presented. The behaviour of Fienup's hybrid input-output phase retrieval algorithm, when it operates on appreciably contaminated data, is demonstrated. The image error, which expresses the violation of the image-space constraints, is shown to exhibit pronounced fluctuations. It is demonstrated that significantly improved final image-forms are obtained by appropriately averaging the image-forms generated at those iterations for which the image error has locally minimum value. A technique for reducing the computational requirements of Fienup's hybrid input-output algorithm is introduced and demonstrated. This technique involves initially estimating the phases of low spatial frequency components of the image, by operating on a fraction of the total number of available Fourier magnitude samples. The number of magnitude samples on which the algorithm operates is increased as the iterations proceed, until all of the available samples are employed. An alternative input-output algorithm is presented, which comprises an appropriate combination of Fienup's basic and hybrid input-output algorithms. It is demonstrated that the performance of this algorithm is superior to that of the hybrid input-output algorithm, in situations where positivity is the only constraint that can be enforced in image space. A phase retrieval algorithm is proposed which employs simulated annealing. Unlike the existing simulated annealing phase retrieval algorithm, in which samples of the image are perturbed, this new algorithm operates by perturbing the phases of the Nyquist samples in Fourier space. A new blind deconvolution algorithm, which invokes simulated annealing, is presented. It is demonstrated that this algorithm is capable of effecting the blind deconvolution of contaminated convolution data. An algorithm is presented and illustrated for directly (i.e. non-iteratively) blindly deconvolving the convolution of two images, where each image comprises a collection of points. A related algorithm is introduced, specifically for effecting the blind deconvolution of ghosted shift-and-add images of star clusters. The performance of this algorithm, when operating on shift-and-add images computed from simulated speckle data, is demonstrated.