We consider the dissipative charging process of quantum batteries in terms of a collisional model, where the batteries are coupled to a heat bath using nonenergy preserving interactions. First, we show that for low temperatures, the collective process can attain a charging power that increases polynomially with the number of batteries. The scaling we find is N3 which, while being greater than the bound obtained for unitary processes, has a lower efficiency. Then, we study the dissipative charging process of a single battery using a time-dependent Hamiltonian that generates coherences in the energy basis. In this case, we find that the presence of coherence could enhance the charging power and also its efficiency. Finally, we show how this process can be used in a quantum heat engine that contains the charging process as one of its open strokes.