Metal halide perovskites (MHPs) are mixed electronic-ionic semiconductors with a remarkable photovoltaic potential that has led to a current world record efficiency surpassing 23%. This good performance stems from the combination of excellent light harvesting and relatively slow nonradiative recombination, which are characteristic of MHPs. However, taking advantage of these properties requires electron and hole transport materials that can efficiently extract charge with minimal photovoltage losses and recombination. It is well-known that n-type anatase TiO2 is a good electron-selective contact (ESC), although the fundamental reasons for its functioning are not completely clear to date. In this Letter, we investigate this issue by preparing perovskite-based solar cells with various n-type metal-oxide electron-selective contacts of different chemical nature and crystal structure. Our main finding is that the open-circuit photovoltage remains essentially independent of the nature of the contact for highly selective electron contacts, a fact that we attribute to a recombination rate that is mainly governed by the bulk of the MHPs. In contrast, replacement of the "standard" TiO2 contact by alternative contacts leads to lower short-circuit photocurrents and more pronounced hysteresis, related to enhanced surface recombination at less effective electron-selective contacts.