The aim of this study is to provide a comprehensive review of the finite element absolute nodal coordinate formulation, which can be used to obtain efficient solutions to large deformation problems of constrained multibody systems. In particular, important features of different types of beam and plate elements that have been proposed since 1996 are reviewed. These elements are categorized by parameterization of the elements (i.e., fully parameterized and gradient deficient elements), strain measures used, and remedies for locking effects. Material nonlinearities and the integration of the absolute nodal coordinate formulation to general multibody dynamics computer algorithms are addressed with particular emphasis on visco-elasticity, elasto-plasticity, and joint constraint formulations. Furthermore, it is shown that the absolute nodal coordinate formulation has been applied to a wide variety of challenging nonlinear dynamics problems that include belt drives, rotor blades, elastic cables, leaf springs, and tires. Unresolved issues and future perspectives of the study of the absolute nodal coordinate formulation are also addressed in this investigation.