Amorphous materials include soft solids such as colloids, emulsions, foams, gels, and granular matter, as well as harder materials such as molecular, polymeric and metallic glasses. In contrast to crystalline solids, the internal arrangement of their constituent microstructures (emulsion droplets, sand grains, etc.) lacks long ranged order. Understanding the rheology (deformation and flow properties) of these materials thus poses a significant challenge. Typically, they show elastic response or slow creep at low loads but yield plastically at larger loads. In this talk, I shall summarise recent progress in understanding the yielding transition between an initially solid-like state and a finally fluidised one, as a function the of time since the imposition of an imposed strain or load. A particular focus will be on the fact that yielding can be highly delayed after the inception of the shear, and on the phenomenon of strain localisation during the dynamical process of yielding.