An increasing number of phasor measurement units (PMUs) are being deployed in power systems in order to enhance the situational awareness and, in the near future, we expect that many networks will be extensively equipped with PMUs. These devices provide accurate and synchronized voltage/current phasors (called synchrophasors) at a reporting rate up to 60 measurements-per-second, which is a significantly different type of information with respect to the commonly-used voltage/current magnitude and power measurements of remote terminal units (RTUs). PMUs are commonly associated with transmission systems, but are gaining consideration also in the context of distribution networks in order to implement fast control schemes due to the presence of highly-volatile distributed generation and for fault location purposes. Power-system state estimation (SE) is a functionality that might largely benefit from the use of synchrophasor measurements. Best current practice consists in estimating the state every few tens of seconds (or even minutes) by using asynchronous measurements of RTUs. A measurement infrastructure exclusively composed of PMUs allows SE to become a linear and not iterative process characterized by a refresh-rate of tens of estimates-per-second and sub-second time-latency. This is what we call real-time SE. Even if SE is a well-established power-system function, it still deserves research in view of the proliferation of PMUs. Improvements in terms of accuracy, computational time and time-latency are required in order to make SE suitable for a wide range of applications, from control to fault management. In this dissertation, we first describe in detail the advantages of using exclusively synchrophasor measurements for the most common SE algorithms, i.e., weighted least squares (WLS), least absolute value (LAV) and Kalman filter (KF). Then, we propose two methods for the on-line estimation of the process-model uncertainties used by the KF, because power-system operating conditions are continuously varying. Our goal is to improve the estimation accuracy by effectively filtering the measurement noise. We designed a heuristic method for quasi-static conditions and a rigorous method that is also able to deal with step changes of the system state. Zero-injections represent equality constraints in the SE problem. We propose a method based on LQ-decomposition for linear WLS-SE that strictly satisfies the equality constraints while reducing the state-vector dimension by the number of constraints. Therefore, the computational time is significantly reduced and the problem becomes less ill-conditioned. An important contribution of this dissertation consists in the validation of the theoretical findings via real-scale experiments. We deployed PMUs at every bus in two real power-systems located in Switzerland. First, we demonstrate the practical feasibility of running SE at high refresh-rate (50 estimates-per-second) and low time-latency (below 70 ms). Second, we compare and discuss the results of WLS, LAV and KF by using real synchrophasor measurements. Finally, we intend to prove that PMU-based real-time SE exhibits unique accuracy, refresh rate and time-latency, which satisfy the requirements of fault location and, potentially, protective relaying. We propose a fault detection and faulted-line identification method based on WLS-SE, which works for any network and fault type as well as in presence of large amount of distributed generation.