We almost certainly agree that the harnessing of electricity can be considered the most important technological advance of the twentieth century. The development that allows this control is the power grid, an intricate system composed of generators, substations and transformers connected by cable lines hundreds of kilometers long. Its presence is nowadays so intertwined with ours, and so much taken for granted, that we are only capable of sensing its absence, disguised as a cascading failure or a blackout in its extreme form. Since these extreme phenomena seem to have increased in recent years and new actors, like highly liberalized markets or environmental and social constraints, are taking a leading role, different paths other than traditional engineering ones have been explored. In the last ten years, and mainly due to increasing computational capability and accessibility to data, the conceptual frame of complex networks has allowed different approaches in order to understand the usual (and not-so-usual) outcomes of this system. This paper considers power grids as complex networks. It presents some recent results that correlate their topology with their fragility, together with major malfunctions analysis, and for the European transmission power grid in particular.