We study numerically and analytically the behaviour of vortex matter in artificial flow channels confined by pinned vortices in the channel edges (CEs). The critical current density Js for channel flow is governed by the interaction with the static vortices in the CEs. Motivated by early experiments which showed oscillations of Js on changing (in)commensurability between the channel width w and the natural vortex row spacing b0, we study structural changes associated with (in)commensurability and their effect on Js and the dynamics. The behaviour depends crucially on the presence of disorder in the arrays in the CEs. For ordered CEs, maxima in Js occur at commensurability w = nb0 (n is an integer), while for w ≠ nb0 defects along the CEs cause a vanishing Js. For weak disorder, the sharp peaks in Js are reduced in height and broadened via nucleation and pinning of defects. The corresponding structures in the channels (for zero or weak disorder) are quasi-1D n row configurations, which can be adequately described by a (disordered) sine-Gordon model. For larger disorder, matching between the longitudinal vortex spacings inside and outside the channel becomes irrelevant and, for w ≃ nb0, the shear current Js levels at ∼30% of the value Js0 for the ideal commensurate lattice. Around ‘half filling’ (w/b0 ≃ n ± 1/2), the disorder leads to new phenomena, namely stabilization and pinning of misaligned dislocations and coexistence of n and n ± 1 rows in the channel. At sufficient disorder, these quasi-2D structures cause a maximum in Js around mismatch, while Js smoothly decreases towards matching due to annealing of the misaligned regions. Near threshold, motion inside the channel is always plastic. We study the evolution of static and dynamic structures on changing w/b0, the relation between the Js modulations and transverse fluctuations in the channels and find dynamic ordering of the arrays at a velocity with a matching dependence similar to Js. We finally compare our numerical findings at strong disorder with recent mode-locking experiments, and find good qualitative agreement.