Situational-awareness methods and technologies are crucial elements to ensure power systems reliability and security as they are used by automated decision-making processes of mission-critical applications. Inadequate system monitoring results in incorrect or delayed actions that may potentially lead to unsafe and unstable evolution of the grid state. The distributed and time-synchronized sensing of the so-called synchrophasors is becoming increasingly adopted by systems operators especially when they plan the refurbishment of their electrical grids with Phasor Measurement Units (PMU) that provide highly accurate, low latency, and high refresh-rate estimates of voltage and current phasors. However, the concept of synchrophasor is based on a static signal model and, therefore, it provides a reliable estimation of the monitored power system signal only for quasi-steady-state conditions. Given the massive integration of inverter-connected renewable energy resources that, as such, do not provide any inertia to the system, modern electrical grids are expected to experience larger dynamics, high shares of harmonic and inter-harmonic pollution, and unprecedented electromechanical transients. Processing tools able to correctly and timely track these conditions, are certainly needed as they may enhance the overall power system situational awareness and its associated security. Within this context, this Thesis proposes advanced synchrophasor networks for the monitoring and control of power grids operating in close-to-stationary conditions. More specifically, enhanced processing tools able to accurately and timely estimate the synchrophasors using extremely short observation intervals are proposed. The methods are based on the discrete Fourier transform and on the Hilbert transform. The compliance of the proposed methods with respect to international standards for measurement and protection applications is verified (IEEE Std. C37.118). The integration of the proposed algorithms into hardware platforms demonstrates their prospective deployability into a new PMU prototype. Further, the developed PMU is synchronized with respect to time using cutting-edge time dissemination technologies like the one provided by the White Rabbit protocol. The superior accuracy in estimating the synchrophasors provided by the algorithms and the PMU devices developed in this Thesis, calls for a calibration process of exceptional performance. In this view, the hardware and software architecture of an advanced validation platform for PMU type-testing is presented and metrologically characterized. Finally, the seamless streaming of synchrophasor data over the underlying communication infrastructure is investigated by considering wired and wireless physical layers and by proposing a time-deterministic phasor data concentrator. For power systems operating in non-stationary operating conditions, the Thesis proposes an innovative approach for the modeling of reduced-inertia electrical grids that goes beyond the concept of static phasor. The study is inspired by the theory on analytic signals and is based on the Hilbert transform that enables the modeling of dynamic signals. A theoretical formulation is outlined and validated over real-world datasets, demonstrating the effectiveness of Hilbert transform-based methods. These results may contribute to the development of novel sensing technologies and may yield to a disruptive innovation in the field of power systems modeling.