Materials properties are ultimately determined by the nature of the interactions between the atoms that form the material. On surfaces, the site-specific spatial distribution of force and energy fields governs the phenomena encountered. This article reviews recent progress in the development of a measurement mode called three-dimensional atomic force microscopy (3D-AFM) that allows the dense, three-dimensional mapping of these surface fields with atomic resolution. Based on noncontact atomic force microscopy, 3D-AFM is able to provide more detailed information on surface properties than ever before, thanks to the simultaneous multi-channel acquisition of complementary spatial data such as local energy dissipation and tunneling currents. By illustrating the results of experiments performed on graphite and pentacene, we explain how 3D-AFM data acquisition works, what challenges have to be addressed in its realization, and what type of data can be extracted from the experiments. Finally, a multitude of potential applications are discussed, with special emphasis on chemical imaging, heterogeneous catalysis, and nanotribology.