Hot-melt extrusion is commonly applied for forming products, ranging from metals to plastics, rubber and clay composites. It is also increasingly used for the production of pharmaceuticals, such as granules, pellets and tablets. In this context, mathematical modeling plays an important role to determine the best process operating conditions, but also to possibly develop software sensors or controllers. The early models were essentially black-box and relied on the measurement of the residence time distribution. Current models involve mass, energy and momentum balances and consists of (partial) differential equations. This paper presents a literature review of a range of existing models. A common case study is considered to illustrate the predictive capability of the main candidate models, programmed in a simulation environment (e.g., MATLAB). Finally, a comprehensive distributed parameter model capturing the main phenomena is proposed.