Welding processes are a fundamental part of modern engineering manufacturing. The simulation of materials joining techniques requires the application of thermal models capable of mathematically describing the applied heat source distribution. Many different approaches have been developed since the beginning of the CFD revolution. However, one of the most important published works regarding the review and detailing of heat source models was performed almost two decades ago. Hence, the present work was developed specifically focusing on organizing, cataloging, describing, and statistically quantifying the most relevant models already published, with a special focus on the techniques developed in the last twenty years. The reviewed approaches were individually listed concerning their most common applications and limitations. The gathered data includes classified details and condensed information about scientific references, the suitability of each model, and the welding heat source thermal modeling terminology. Additionally, each modeling form was geometrically illustrated in coupling with its equations for an enhanced description and comparison of the geometrical parameters and its expected resultant temperature distributions. The reviewed papers were quantified and statistically enumerated by modeling methodology, welding process type, and number of published works by year. The approaches were also organized chronologically and visually illustrated in a welding heat source modeling timeline. Lastly, the most relevant achievements of the last decades, the research trends, and possibilities for future review works in the field were discussed.