State estimation problem for power systems has long been a fundamental issue that demands a variety of methodologies depending on the system settings. With the recent introduction of advanced devices of phasor measurement units (PMUs) and dedicated communication networks, the infrastructure of power grids has been greatly improved. Coupled with the infrastructure improvements are three emerging issues for the state estimation problems, namely, the coexistence of both traditional and PMU measurements, the incomplete information resulting from delayed, asynchronous and missing measurements due to communication constraints, and the cyber-attacks on the communication channels. In this study, the authors aim to survey some recent advances on the state estimation methods which tackle the above three issues in power grids. Traditional state estimation methods applied in power grids are first introduced. Latest results on state estimation with mixed measurements and incomplete measurements are then discussed in great detail. In addition, the techniques developed to ensure the cyber-security of the state estimation schemes for power grids are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out.