Self-healing is capacity of the network to restore automatically the network when an outage occurs. Smart grids makes power restoration on the one hand more complex due to distributed generation, distributed storage and mobile loads (electrical vehicles), but on the other hand the observability is improved with the introduction of smart meters and IEDs (intelligent electronic devices). The relevant differences between traditional distribution networks and smart grids for power restoration are reviewed. This paper formulates the problem of self-healing in smart grids. Furthermore, the network features and constraints are explained. Moreover, the restoration goals are given. In short the contribution of this paper are: a definition of self-healing, the formalization of this concept (graph, constraints, goals), a description of the relevant smart grid features and discussion of the complexity of the problem.