  We use atomistic computer simulations to provide a microscopic description of
the brittle failure of amorphous materials and assess the role of rare events
and quenched disorder. We argue that brittle yielding originates at rare soft
regions, similarly to Griffiths effects in disordered systems. We numerically
demonstrate how localised plastic events in such soft regions trigger
macroscopic failure via the propagation of a shear band. This physical picture,
which no longer holds in poorly annealed ductile materials, allows us to
discuss the role of finite-size effects in brittle yielding and reinforces the
similarities between yielding and other disorder-controlled nonequilibrium
phase transitions such as depinning and hysteresis.
