A review is presented of the earliest stages of protostellar evolution. Observations of prestellar cores, which are believed to represent the initial conditions for protostellar collapse, depart significantly from the scale-free density distribution which is usually taken as the starting point for the formation of a low-mass protostar. Pre-stellar cores are observed to have radial density profiles which have flat inner regions, steepening towards their edges. This is seen to qualitatively match the predictions of the Bonnor-Ebert stability criterion for pressure-bounded self-gravitating gas clouds. From these initial conditions, theoretical modelling of cores threaded by magnetic fields predicts that quasi-static evolution by the process of ambipolar diffusion will lead to a significantly different starting point for collapse than the static singular isothermal sphere. This departure from a scale-free density distribution for the initial conditions has recently been shown to produce an ensuing protostellar collapse which has a non-constant accretion rate. Recently published observations of low-mass protostars in the ρ Ophiuchi cluster are demonstrated to be consistent with such a non-constant protostellar mass accretion rate, contrary to the standard protostellar collapse model. Instead, the data appear consistent with an initially high accretion rate, which subsequently decays. The initial phase of high accretion rate is labelled the ‘main accretion phase’, during which ≥50 per cent of the circumstellar envelope mass is accreted in ∼10 per cent of the total accretion time, and which is equated observationally with Class 0 objects. The subsequent phase with roughly an order of magnitude lower accretion rate is labelled the ‘late accretion phase’, during which the remainder of the envelope mass is accreted in the remaining ∼90 per cent of the total accretion time, at an order of magnitude lower accretion rate, and which is equated observationally with Class I objects. The growth of circumstellar discs begins in the Class 0 stage, and proceeds through the Class I and II stages. Published data of the Taurus star-forming region currently available appear also to be consistent with this scenario.