The challenges currently faced by network operators are difficult and complex. Presently, various types of energy sources with random generation, energy storage units operating in charging or discharging mode and consumers with different operating characteristics are connected to the power grid. The network is being expanded and modernised. This contributes to the occurrence of various types of network operating states in practice. The appearance of a significant number of objects with random generation in the power system complicates the process of planning and controlling the operation of the power system. It is therefore necessary to constantly search for new methods and algorithms that allow operators to adapt to the changing operating conditions of the power grid. There are many different types of method in the literature, with varying effectiveness, that have been or are used in practice. So far, however, no one ideal, universal method or methodology has been invented that would enable (with equal effectiveness) all problems faced by the power system to be solved. This article presents an overview and a short description of research works available in the literature in which the authors have used modern methods to solve various problems in the field of power engineering. The article is an introduction to the special issue entitled Advances in the Application of Methods Based on Artificial Intelligence and Optimisation in Power Engineering. It is an overview of various current problems and the various methods used to solve them, which are used to cope with difficult situations. The authors also pointed out potential research gaps that can be treated as areas for further research.