Bridge piers in a flow cause a horizontal constriction of the flow, comparable to that caused by abutments. The local scour around bridge piers depends strongly on the geometry of the pier. Local scour around a bridge pier is usually a relatively rapid process. The chapter discusses distinctive parameters of bridge piers that influence the scour process. The process of local scour around bridge piers can be divided into several phases: initial phase, development phase, stabilisation phase and equilibrium phase. In general, local scour around bridge piers is a relatively rapid process. For slender bridge piers the influence of the flow depth is marginal. According to B. Dargahi, the slope of a scour hole around a bridge pier can be divided into three regions: upper and lower regions and, in the deepest part of a scour hole, a concave region.