The variability and distributed nature of renewable energy sources (RES) pose challenges to real-time monitoring and control in distribution networks. Phasor measurement units (PMUs) provide high-precision, time-synchronized measurements, significantly improving state estimation (SE) accuracy in complex grids. This paper reviews SE in distribution systems using PMU data, focusing on challenges introduced by high-RES integration. Traditional techniques, such as weighted least squares (WLS), are analyzed, revealing limitations like reduced observability and accuracy due to RES intermittency. To address these challenges, advanced methods such as robust optimization, dynamic network reconfiguration, and decentralized control are explored, showing improved network reliability and adaptability under RES variability. Furthermore, innovative approaches like Bayesian non-parametric modelling are discussed, offering solutions to mitigate uncertainties and enhance grid flexibility. Case studies highlight the scalability and effectiveness of PMUs in extensive networks, showcasing their role in improving both SE precision and system stability. These findings underline the critical need for precise and integrated SE techniques to develop resilient, adaptable smart grids capable of accommodating the increasing penetration of RES, setting a foundation for future technological advancements.