Sloping terrain distorts the sun-target–sensor geometry, resulting in biases of the optical reflectance measured by remote sensors relative to flat situations. Performing topographic correction (TC) is, therefore, deemed mandatory to foster the full exploitation of satellite images worldwide to support various applications in mountainous regions. Various TC models have already been proposed and developed, while most of them were previously evaluated at local or regional scales using a few images with various evaluation criteria. Therefore, a systematic and comprehensive assessment has yet to be done on these TC models in the global mountainous regions. In the present study, 10 523 Landsat 8 Operational Land Imager (OLI) images, filtered by land cover types and seasons and sampled across global mountain regions, were corrected using ten popular TC models—statistical empirical (SE), b correction, variable empirical coefficient algorithm (VECA), C-correction (CC), sun-canopy–sensor (SCS), DymondShepherd (DS), SCS + C, path length correction (PLC), Minnaert, and Minnaert + SCS—with a unified evaluation criterion on the Google Earth Engine (GEE) platform. The outcomes are that: 1) global TC effects on Landsat 8 OLI images generally increase with sun zenith angles (SZAs) and latitudes; 2) six models (SE, b correction, CC, VECA, Minnaert, and Minnaert + SCS) show good adaptability among the ten models for the global mountainous placing a disregard to land cover types and seasons; and 3) considering permanent snow and ice, needle-leaved forests in winter, and null values might appear in b correction, SE is deemed to be with the most global adaptability. This study pioneers an evaluation of fashionable TC models concerning mountainous regions worldwide and will be useful for applying TC to Landsat images for the benefit of making global TC products in the future and a fair intercomparison of OLI surface reflectance measured in various mountainous areas of the globe.