A liquid free surface in partially filled containers can experience a wide spectrum of motions such as planar, non-planar, rotational, quasi-periodic, chaotic, and disintegration. Civil engineers and seismologists have been studying liquid sloshing effects on large dams, oil tanks and elevated water towers under ground motion. Since the early 1960’s, the problem of liquid sloshing dynamics has been of major concern to aerospace engineers studying the influence of liquid propellant sloshing on the flight performance of jet vehicles. Since then, new areas of research activities have emerged. The modern theory of nonlinear dynamics has indeed promoted further studies and uncovered complex nonlinear phenomena. These include rotary sloshing, Faraday waves, nonlinear liquid sloshing interaction with elastic structures, internal resonance effects, stochastic sloshing dynamics, hydrodynamic sloshing impact dynamics, g-jitter under microgravity field, cross-waves, and spatial resonance. The dynamic stability of liquid gas tankers and ship cargo tankers, and liquid hydrodynamic impact loading are problems of current interest to the designers of such systems. This article will address the means of passive control of liquid sloshing and the use of liquid sloshing forces to control vibratory structures. Other important contributions include the development of digital computer codes to solve complex problems that were difficult to handle in the past. The purpose of this article is to review the research work developed in different applications. It will highlight the major achievements and results reported in the literature. Some early work will be cited very briefly in order to provide an updated bibliography of liquid sloshing dynamics. This review article contains 1,319 references.