This report presents an in-depth review of the current state of knowledge on hull slamming, which is one of several types of slamming problems to be considered in the design and operation of ships. Hull slamming refers to the impact of the hull or a section of the hull as it reenters the water. It can be considered to be part of a larger class of water entry problems that include the water landing of spacecraft and solid rocket boosters, the water landing and ditching of aircraft, ballistic impacts on fuel tanks, and other applications. The problem involves the interaction of a structure with a fluid that has a free surface. Significant simplifications can be achieved by considering a two-dimensional cross section of simple shape (wedge, cone, sphere, and cylinder) and by assuming that the structure is a rigid body. The water is generally modeled as an incompressible, irrotational, inviscid fluid. Two approximate solutions developed by von Karman (1929, “The Impact on Seaplane Floats During Landing,” NACA Technical Note NACA-TN-32) and Wagner (1932, “Uber stoss und Gleitvorgange an der Oberache von Flussigkeiten,” Z. Angew. Math. Mech., 12, pp. 192–215) can be used to predict the motion of the body, the hydrodynamic force, and the pressure distribution on the wetted surface of the body. Near the intersection with the initial water surface, water piles up, a jet is formed, and the solution has a singularity in this region. It was shown that nearly half of the kinetic energy transferred from the solid to the fluid is contained in this jet, the rest being stored in the bulk of the fluid. A number of complicating factors are considered, including oblique or asymmetric impacts, elastic deformations, and more complex geometries. Other marine applications are considered as well as applications in aerospace engineering. Emphasis is placed on basic principles and analytical solutions as an introduction to this topic, but numerical approaches are needed to address practical problems, so extensive references to numerical approaches are also given.