In the last decade, a range of new remote-sensing techniques has led to a dramatic increase in terrain information, providing new opportunities for a better understanding of Earth surface processes based on geomorphic signatures. Technologies such as airborne and terrestrial lidar (Light Detection and Ranging) to obtain high-resolution topography have opened avenues for the analysis of landslides, hillslope and channellization processes, river morphology, active tectonics, volcanic landforms and anthropogenic signatures on topography. This review provides an overview of the recent flourishing literature on high-resolution topographic analyses, underlining their opportunities and critical issues such as their limitations. The goal is to provide answers to questions such as what kind of processes can be analyzed through high-resolution topographic data and how to do it. The review focuses on two different environments: natural and engineered landscapes. In both contexts, high-resolution topography offers opportunities to better understand geomorphic processes from topographic signatures. Particular attention is given to engineered landscapes in which the direct anthropic alteration of processes is significant. The last part of the review discusses future challenges.