The last two decades have seen significant advances in our understanding of the mechanisms of plasticity and flow in amorphous solids and supercooled liquids. In the solid, irreversible deformations result from the accumulation of local rearrangements that are controlled by the crossing of global elastic instabilities, largely determined by local yield stress heterogeneities. These rearrangements create in their surroundings elastic strains that may trigger secondary events, thus leading to the emergence of plastic avalanches that are clearly separated from each other in athermal quasi-static conditions. A main surprise has been the realization that such events and correlations between them (i.e. a form of avalanche behavior) continue to exist at finite strain rate and finite temperature up into the Newtonian liquid regime. Thus event-event correlations play a crucial role in determining non-Newtonian behavior. Moreover, these ideas further document the view that the flow of highly viscous liquids proceeds by a series of hops between inherent states, which are local minima of the potential energy surface, and hence mechanically equilibrated solids. Thus, up into the liquid, flow can be viewed as resulting from the accumulation of solid-solid (Eshelby) transformations.