Optimal power flow problems and market clearing approaches are converging: cost-optimal scheduling of loads and generators should be performed while taking the grid’s physics and operational envelopes into account. Within the SmartNet project, the idea is to consider the grid’s physical behaviour in market clearing approaches. Taking the physics of power flow into account, while managing solution times, demands pragmatic approaches. Convex relaxation and linear approximation are two such approaches to manage computational tractability. This work gives an overview of recent OPF formulations, and their relaxations and approximations. The hierarchy of the approaches is detailed, as well as the loss of properties resulting from the relaxation process.