In Ihe firs! article of (his volume Thomson presents a comprehensive analysis of the long-standing problem of how solids fracture, wiih emphasis on the atomistic features of especial interest to physicists. Important questions dealt with include what determines mechanical toughness and whether the fracture will be brittle or ductile. It is shown that the answers to these questions require an understanding of the interactions between dislocations and cracks. These interactions are analyzed in detail.