The focus of this thesis is to design and implement distributed and decentralized state estimation (SE) algorithms for smart Electric Power Grids (EPGs). These algorithms are applied to two different types of EPGs: 1) modern, deregulated transmission networks that include advanced wide-area monitoring systems, and; 2) smart distribution networks with high penetration of distributed and renewable generation (DG) configured of microgrids. Microgrids are capable of cutting off from the main grid and operating autonomously in the islanded mode of operation in case of emergency situations. SE in such systems is complex because of highly non-linear system dynamics, slow and corrupted measurement updates, as well as the sheer computational complexity of the estimation algorithms. The contribution of this thesis is to explore the design and implementation of a reduced-order, distributed particle filter for state estimation in EPGs. Knowledge of the EPG state is necessary for EPG control, optimization, and emergency troubleshooting