Disordered systems typically respond non-smoothly to external driving.  This manifests itself in Barkhausen noise, earthquakes and avalanches in granular media.  A simple classical model which describes such phenomena quite accurately is a particle driven by a spring on a Brownian random-force landscape (also known as the ABBM model).  I will present some analytical results on statistics of avalanches in this model.  I will then show how the ABBM model arises as the mean-field limit of a spatially extended elastic interface in a disordered environment. In the end I will discuss the behavior below the upper critical dimension using renormalization-group methods.