Modern power engineering is struggling with various problems that have not been observed before or have occurred very rarely. The main cause of these problems results from the increasing number of connected distributed electricity sources, mainly renewable energy sources (RESs). Therefore, energy generation is becoming more and more diverse, both in terms of technology and location. Grids that have so far worked as receiving networks change their original function and become generation networks. The directions of power flow have changed. In the case of distribution networks, this is manifested by power flows towards transformer stations and further to the network with a higher voltage level. As a result of a large number of RESs, their total share in the total generation increases. This has a significant impact on various aspects of the operation of the power system. Voltage profiles, branch loads, power flows and directions of power flows between areas change. As a result of the random nature of RES generation, there are problems with the quality of electricity, source stability issues, branch overloading, voltage exceedances and power balance. The occurrence of various types of problems requires the use of more and more advanced methods to solve them. This review paper, which is an introduction to the Special Issue Advanced Optimisation and Forecasting Methods in Power Engineering, describes and justifies the need to reach for effective and available mathematical and IT methods that are necessary to deal with the existing threats appearing in the operation of modern power systems. It indicates exemplary, current problems and advanced methods to solve them. This article is an introduction and justification for the use of advanced calculation methods and algorithms. Engineering intuition and experience are often not enough due to the size and complexity of power grid operation. Therefore, it becomes necessary to use methods based on artificial intelligence and other advanced solutions that will facilitate and support decision making in practice.