We discuss the physics of fracture in terms of the statistical physics associated with the failure of elastic media under applied stresses in presence of quenched disorder. We show that the development and the propagation of fracture are largely determined by the strength of the disorder and the stress field around them. Disorder acts as nucleation centres for fracture. We discuss Griffith's law for a single crack-like defect as a source for fracture nucleation and subsequently consider two situations: (i) low disorder concentration of the defects, where the failure is determined by the extreme value statistics of the most vulnerable defect (nucleation regime) and (ii) high disorder concentration of the defects, where the scaling theory near percolation transition is applicable. In this regime, the development of fracture takes place through avalanches of a large number of tiny microfractures with universal statistical features. We discuss the transition from brittle to quasi-brittle behaviour of fracture with the strength of disorder in the mean-field fibre bundle model. We also discuss how the nucleation or percolation mode of growth of fracture depends on the stress distribution range around a defect. We discuss the corresponding numerical simulation results on random resistor and spring networks. This article is part of the theme issue ‘Statistical physics of fracture and earthquakes’.