Liquid containers constitute major components in a number of dynamical systems such as aerospace vehicles, road tankers, liquefied natural gas carriers, and elevated water towers. The dynamic behavior of these systems is greatly affected by the dynamics of the free liquid surface. The basic problem of liquid sloshing involves the estimation of hydrodynamic pressure distribution, forces, moments and natural frequencies of the free liquid surface. These parameters have direct effect on the dynamic stability and performance of moving containers. The aerospace technology has promoted the research activities in many problems pertaining to liquid sloshing and the special NASA research monograph edited by Abramson [1] documents these problems. Recently, Ibrahim, et al, [2] presented an extensive review of recent advances in liquid sloshing dynamics and the present paper is an abridged form. 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. 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 or jet vehicles. Since then, new areas of research activities have emerged. Thft modem 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.