The resurgence of airships has created a need for dynamics models and simulation capabilities adapted to these lighter-than-air vehicles. However, the modeling techniques for airship dynamics have lagged behind and are less systematic than those for fixed-wing aircraft. A state-of-the-art literature review is presented on airship dynamics modeling, aiming to provide a comprehensive description of the main problems in this area and a useful source of references for researchers and engineers interested in modern airship applications. The references are categorized according to the major topics in this area: aerodynamics, flight dynamics, incorporation of structural flexibility, incorporation of atmospheric turbulence, and effects of ballonets. Relevant analytical, numerical, and semi-empirical techniques are discussed, with a particular focus on how the main differences between lighter-than-air and heavier-than-air aircraft have been addressed in the modeling. Directions are suggested for future research on each of these topics.