Biomedical imaging at microwave frequencies has shown potential for breast cancer detection and monitoring. The advantages of microwave imaging over current imaging techniques are that it is relatively inexpensive, and uses low-energy, non-ionizing radiation. It also provides a quantitative measurement of the dielectric properties of tissues, which offers the ability to characterize tissue types. Microwave imaging also comes with significant drawbacks. The resolution is poor compared to other imaging modalities, which presents challenges when trying to resolve fine structures. It is also not very sensitive to low contrast objects, and the accuracy of recovered tissue properties can be poor. This thesis shows that the use of prior information in microwave imaging inversion algorithms greatly improves the resulting images by minimizing mathematical difficulties in reconstruction that are due to the ill-posed nature of the inverse problem. The focus of this work is to explore novel methods to obtain and use prior information in the microwave breast imaging problem. We make use of finite element contrast source inversion (FEM-CSI) software formulated in two and three dimensions (2D, 3D). This software has the ability to incorporate prior information as an inhomogeneous numerical background medium. We motivate the usefulness of prior information by developing a simulated annealing technique that segments experimental human forearm images into tissue regions. Tissue types are identified and the resulting map of dielectric properties is used as prior information for the 2D FEM-CSI code. This results in improvements to the reconstructions, demonstrating the ability of prior information to improve breast images. We develop a combined microwave tomography/radar algorithm, and demonstrate that it is able to reconstruct images of superior quality, compared to either technique used alone. The algorithm is applied to data from phantoms containing tumours of decreasing size and can accurately monitor the changes. The combined algorithm is shown to be robust to the choice of immersion medium. This property allows us to design an immersion medium-independent algorithm, in which a numerical background can be used to reduce the contrast. We also develop a novel march-on-background technique that reconstructs high quality images using data collected in multiple immersion media. / October 2016