To counter climate change, modern power systems are undergoing a decarbonisation-based transition involving vast deployment of renewable energy sources and electrification of societies. For this transition to succeed, various challenges associated with renewable power production need to be addressed in power system operations. These challenges stem from high output variability along with limited predictability and controllability, leading to flexibility needs in power system operations. Optimal power flow (OPF) and unit commitment (UC) are amongst the most important computational tools for system operators to determine the state of the power system. This computation is performed to optimise various decisions on the grid, to dispatch the components in the network, and to reconfigure them. Additionally, the computation is used to price the services provided by large scale generators and, progressively, by decentralised entities such as households and small enterprises which, apart from consuming, also generate and store power, and thus, have a role in energy balancing through their flexibility. Various simplifications are made in OPF and UC to tackle the computational burden of the models, which tends to be high for realistic systems. Model inaccuracy due to simplification of power flow equations or ignoring stochasticity, is increasingly causing high costs for system operations, as the real situation deviates from the forecast implying costly actions by system operators in real-time. This thesis focuses on challenges in modern power system operations, such as coordinated congestion and voltage management, energy and reserve scheduling as well as price computation. Firstly, the thesis constructs methods and algorithms to enhance computational capability and model accuracy for Alternating Current (AC) Network-Constrained UC and OPF problems through devising an improved approximation of the physical laws governing power flows. Secondly, it applies these methods and algorithms to the coordination problem amongst multiple Distribution System Operators (DSO) and Transmission System Operators (TSO), introducing novel decentralised optimisation techniques for managing congestion and voltage problems as well as addressing network information exchange aspects. Finally, the thesis proposes new pricing mechanisms, endogenously tackling the non-convex operational decisions for energy and reserve scheduling for day-ahead planning, considering stochasticity of renewable energy generation. Computational and accuracy benefits are illustrated in case studies by employing various metrics developed.