The evolution from passive to Active Distribution Networks (ADNs) is producing large changes in the operation of these electrical systems. In particular, violations of grid operational constraints, higher dynamics and limited amount of controllable resources represent main limiting factors in the optimal operation of ADNs in presence of massive stochastic distributed generation. In order to deal with these issues, the emergence of ADNs requires the definition of suitable Energy Management Systems to achieve specific operation objectives (i.e., optimal voltage/congestion controls, updated protection schemes etc.). These functions are significantly improved if the system state is known with high accuracy, high refresh rates and low time latencies. Unfortunately, typical refresh rates of traditional State Estimation (SE) processes designed for transmission networks are in the order of few minutes, whereas the time frames of the above functionalities are between few milliseconds to few seconds. Hence, it becomes necessary to define, develop and validate the three-phase Real-Time State Estimation (RTSE) processes characterised by high refresh rates (i.e., in the range of several tens of estimation per second), small latencies (i.e., in the range of few tens of ms) and high accuracy. In this direction, the ADNs SE is facilitated by the emerging technology of Phasor Measurement Units (PMUs) which allow acquiring accurate, time-aligned phasors with typical streaming rates in the order of some tens of f.p.s. Additionally, PMUs measurements of synchrophasors allow formulating the SE problem in a linear way. PMU measurements can be acquired and stored in a real-time (RT) database, provided by Phasor Data Concentrators (PDCs) suitably coupled with the RTSE. This enables, in theory, the performance assessment of the whole RTSE chain. However, the assessment of the RTSE accuracy with real PMUs in a real grid is impossible since the true state is hidden. It is, yet, possible to overcome this limitation by using a Real Time Simulator (RTS) and design a RT setup that allows knowing the true state. This RT setup should be GPS-synchronized, to enable the RTSE accuracy and time latencies assessment. Within the above context, this thesis focuses on the definition of SE methods together with their formal and numerical performance assessment. In particular, the first part of the thesis discusses the formulation of static (e.g., weighted least squares - WLS) and recursive (e.g., Kalman Filter - KF) algorithms fed by synchronized phasors and/or other traditional measurements provided by remote terminal units. Then, the thesis discusses the formal comparison of the accuracy of KF vs. WLS and proves that the former behaves better if its process model is correct. For the case of linear SE, the thesis discusses the method for the verification of the exactness of the so-called measurement noise covariance matrix. The subsequent part of the thesis provides the numerical validation and performance assessment of the RTSE process via offline simulations. This analysis is conducted by using IEEE benchmark distribution and transmission networks as well as real distribution feeders. The last part of the thesis focuses on the experimental validation of the RTSE chain via an experimental RT setup. In this last part, the thesis describes the structure and the individual components simulated in the RT experimental setup as well as the whole validation procedure.