This paper argues for the need to address the issue of multi-channel network performance under constraints on channel switching. We present examples from emergent directions in wireless networking to motivate the need for such a study, and introduce some models to capture channel switching constraints. For some of these models, we study connectivity and capacity of a wireless network comprising n randomly deployed nodes, equipped with a single interface each, when there are c = O(log n) channels of equal bandwidth W/c available. We consider an adjacent (c,f) channel assignment where a node may switch between f adjacent channels, but the adjacent channel block is randomly assigned. We show that the per-flow capacity for this channel assignment model is ⊖(W√f/cn log n). We then show how the adjacent (c,2) assignment maps to the case of untuned radios. We also consider a random (c,f) assignment where each node may switch between a pre-assigned random subset of f channels. For this model, we prove that per-flow capacity is O(w\√prnd/n log n) (where prnd = 1-(1-f/c)(1-f/c-1)...(1-f/c-f+1)) and Ω(W√f/cn log n).