This thesis contributes to the power system restoration (PSR) field by studying (in the aim of improving) the power system repair and restoration (PSRR) which is a novel problem in PSR. The optimisation concept was our approach and mechanism in tackling this topic. The thesis provides a basic contribution to the PSRR field by studying some of its main subjects and presenting improvements to the best practices in the field. This thesis is built on five research papers related to the thesis title. The thesis investigated a large number of high-quality published research papers, and presented a novel, precise, and comprehensive overview of the topic that could be considered a good introduction for anyone who would like to learn the topic. This was presented in chapter two. We have presented a well-developed and easy to understand structure that starts from the basics of PSR and PSRR to their details and relevant subjects. Also, in this thesis we provided application-based studies using mathematical optimisation techniques, where we model a specific power system then solve the PSRR problem aiming optimality. Different optimisation techniques were applied, analysed, and compared for both sides of the problem (i.e. the restoration problem, and the repair problem) as well as different modelling for power systems. Our findings in this chapter were interesting and align with other high-quality studies in the literature. This was presented in details in chapter three. This thesis also tackled a very important relevant subject which is the system reliability under certain restoration scenarios. Where we studied the effects of restoration actions under certain conditions such as cold load pickup events to the reliability indices of the system. A novel Nature-inspired optimisation technique was developed and compared to an old technique that was presented in a high-quality study in the literature. This was presented in chapter four. We concluded this thesis research by developing a statistical analysis for power system outages for a decade period of time in the Australian industry as well as investigating the potential benefits of smart grid technologies and their investments to the power grid. Many statistical methods were applied and investigated using state-of-the-art programming tools. This was presented in chapter five. We have presented very interesting results and findings in this chapter.