This monograph addresses the problem of geometric registration and the classical Iterative Closest Point ICP algorithm. Though commonly used in several research fields, the focus here is on mobile robotics in which point clouds need to be registered. Even with this narrowed focus, the problem is still complex and multiple-faceted. A lot has been published on the topic, and, up until now, it has lacked a general comparison methodology. This is understandable given the diversity of applications, characteristics of the sensors, motion capabilities of the robotic platform and characteristics of the environments, but it hinders the selection process of an appropriate instance of the algorithm. This review tackles this challenge by three means 1 a wide literature review with a historical perspective, 2 the elaboration of a theoretical descriptive framework of geometric registration grounded in the literature review, and 3 the analysis of practical use cases covering a wide diversity of mobil