The evolving complexity of electric power systems with higher levels of uncertainties is a new challenge faced by system operators. Therefore, new methods for power system prediction, monitoring and state estimation are relevant for the efficient exploitation of renewable energy sources and the secure operation of network assets.In order to estimate all possible operating conditions of power systems, this Thesis proposes the use of Gaussian mixture models to represent non-Gaussian correlated input variables, such as wind power output or aggregated load demands in the probabilistic load flow problem. The formulation, based on multiple Weighted Least Square runs, is also extended to monitor distribution radial networks where the uncertainty of these networks is aggravated by the lack of sufficient real-time measurements.This research also explores reduction techniques to limit the computational demands of the probabilistic load flow and it assesses the impact of the reductions on the resulting probability density functions of power flows and bus voltages.The development of synchronised measurement technology to support monitoring of electric power systems in real-time is also studied in this work. The Thesis presents and compares different formulations for incorporating conventional and synchronised measurements in the state estimation problem. As a result of the study, a new hybrid constrained state estimator is proposed. This constrained formulation makes it possible to take advantage of the information from synchronised phasor measurements of branch currents and bus voltages in polar form. Additionally, the study is extended to assess the advantages of PMU measurements in multi-area state estimators and it explores a new algorithm that minimises the data exchange between local area state estimators.Finally, this research work also presents the advantages of dynamic state estimators supported by Synchronised Measurement Technology. The dynamic state estimator is compared with the static approach in terms of accuracy and performance during sudden changes of states and the presence of bad data. All formulations presented in this Thesis were validated in different IEEE test systems.