Channel conditions in wireless networks exhibit huge variations across space and time, giving rise to vast fluctuations in the transmission rates. Channel-aware scheduling strategies provide an effective mechanism for improving throughput performance by exploiting such rate variations, and these have been extensively examined at the packet level for a static user configuration. In this paper, we discuss the performance implications at the flow level for a dynamic user population, taking into account variations on a slower time scale and wide-range user mobility as well. First of all, we present simple necessary conditions for flow-level stability and prove that these are in fact (near) sufficient for a wide family of utility-based scheduling strategies. It is further shown how the flow-level performance of the proportional fair scheduling strategy may be evaluated by means of a processor-sharing model with a state-dependent service rate. In addition, we examine the impact of variations on a slower time scale, and establish that the so-called fluid and quasistationary regimes yield explicit, insensitive performance bounds. Finally, we turn our attention to a network of several base stations (BSs) with handoffs of active sessions governed by wide-range user mobility. It is demonstrated that mobility increases the capacity, not only in the case of globally optimal scheduling but also when each of the BSs adheres to a local fair-sharing discipline.