The realization of very high efficiency, stable perovskite solar cells fabricated on a large scale at low cost, has the potential to further lower the cost of photovoltaics. This necessitates an understanding of the properties required of the perovskite material, including the carrier mobility. Perovskite cells also feature mobile ionic species, and the impact of these ions on cell performance – and in particular, to what extent and under what circumstances they may limit device performance – is not well understood. Here, we employ an advanced numerical model that allows for the presence of mobile ionic species to probe the relationship between carrier mobility, the presence of ionic species as well as different possible recombination mechanisms within the cell. We show that a high electron and hole conductivity throughout the device is key to avoiding transport losses. For devices operating significantly below their radiative limit, achieving a sufficiently high conductivity requires high carrier mobilities of at least 10cm2/V-s. It is shown that the presence of a single mobile ionic species can lead to effective doping of the perovskite bulk, which is detrimental to cell performance by lowering the conductivity of one type of carrier. The results also indicate that increasing cell VOC closer to its radiative limit is also beneficial for reducing transport losses and pushing cell performance closer to its theoretical limit.