Optimal power flow (OPF) problems are non-convex and large-scale optimization problems which appear in operation analysis, scheduling, and energy management of power systems. Various algorithms have been developed to solve the OPF problems, while in many cases, only local optimal solutions are available. Recent studies show that semidefinite programming (SDP) can either provide an exact or near global optima for the OPF problems. In this regard, there are enormous potential for SDP in solving the OPF problems. However, SDP-based approaches are far from real-world implementations. This talk will cover our recent results that partially address the limitations of SDP-based approaches for the OPF, including scalability, incorporation of binary variables, and distributed formulation.