The interpretation of the expanding universe as an expansion of space has recently been challenged. From the geodesic equation in Friedmann universe models and the empty Milne model, we argue that a Newtonian or special relativistic analysis is not applicable on large scales, and the general relativistic interpretation in terms of expanding space has the advantage of being globally consistent. We also show that the cosmic redshift, interpreted as an expansion effect, containts both the Doppler effect and the gravitational frequency shift.