From an extensive search of papers related to the comparison of Global Digital Elevation Models (hereinafter GDEMs), an analysis is carried out that aims to answer several questions such as: Which GDEMs have been compared? Where have the comparisons been made? How many comparisons have been made? How have the assessments been carried out? Which is the GDEM option with the lowest RMSE? Analysis shows that SRTM and ASTER are the most popular GDEMs, that the countries where more comparisons have been made are Brazil, India, and China, and that the main type of reference data for evaluations is the use of points surveyed by GNSS techniques. A variety of criteria have been found for the comparison of GDEMs, but the most used are the RMSE and the standard deviation of the elevation error. There are numerous criteria with a more user-centric character in thematic areas, such as morphometry, geomorphology, erosion, etc. However, in none of the thematic areas does there exist a standard method of comparison. This limits the possibilities of establishing a ranking of GDEMs based on their user-focused quality. In addition, the methods and reference data set are not adequately explained or shared, which limits the interoperability of the studies carried out and the ability to make robust comparisons between them.