The tokamak and the stellarator are the two main candidate concepts for magnetically confining fusion plasmas. The flexibility of the mid-size stellarator devices together with their unique diagnostic capabilities make them ideally suited to study the relation between magnetic topology, electric fields and transport. This paper addresses advances in the understanding of plasma transport in mid-size stellarators with an emphasis on the physics of flows, transport control, impurity and particle transport and fast particles. The results described here emphasize an improved physics understanding of phenomena in stellarators that complements the empirical approach. Experiments in mid-size stellarators support the development of advanced plasma scenarios in Wendelstein 7-X (W7-X) and, in concert with better physics understanding in tokamaks, may ultimately lead to an advance in the prediction of burning plasma behaviour.