The phenomenon of lowering the riverbed level due to removal of sediment is known as scour. In general, scour is classified as general scour, contraction scour, and local scour. This chapter provides a comprehensive discussion on scour within channel contractions, downstream of structures, below horizontal pipelines, at bridge piers, and abutments. Further, scour countermeasures are of paramount importance to river engineers. This issue is also discussed. Numerical examples on prediction of scour depths are worked out. © 2014, Springer-Verlag Berlin Heidelberg.