In the envisioned smart grid, high penetration of uncertain renewables, unpredictable participation of (industrial) customers, and purposeful manipulation of smart meter readings, all highlight the need for accurate, fast, and robust power system state estimation (PSSE). Nonetheless, most real-time data available in the current and upcoming transmission/distribution systems are nonlinear in power system states (i.e., nodal voltage phasors). Scalable approaches to dealing with PSSE tasks undergo a paradigm shift toward addressing the unique modeling and computational challenges associated with those nonlinear measurements. In this study, we provide a contemporary overview of PSSE and describe the current state of the art in the nonlinear weighted least-squares and least-absolutevalue PSSE. To benchmark the performance of unbiased estimators, the Cramér-Rao lower bound is developed. Accounting for cyber attacks, new corruption models are introduced, and robust PSSE approaches are outlined as well. Finally, distribution system state estimation is discussed along with its current challenges. Simulation tests corroborate the effectiveness of the developed algorithms as well as the practical merits of the theory.