Conservative methods for the numerical solution of the Vlasov equation are developed in the context of the one-dimensional splitting. In the case of constant advection, these methods and the traditional semi-Lagrangian ones are proven to be equivalent, but the conservative methods offer the possibility to add adequate filters in order to ensure the positivity. In the non constant advection case, they present an alternative to the traditional semi-Lagrangian schemes which can suffer from bad mass conservation, in this time splitting setting.