| Summary: | Imaging methods based on the absorption or scattering of atmospheric muons, collectively named under the neologism “muography”, exploit the abundant natural flux of muons produced from cosmic-ray interactions in the atmosphere. Recent years have seen a steep rise in the development of muography methods in a variety of innovative multidisciplinary approaches to study the interior of natural or human-made structures, establishing synergies between usually disconnected academic disciplines such as particle physics, geology, and archaeology. Muography also bears promise of immediate societal impact through geotechnical investigations, nuclear waste surveys, homeland security, and natural hazard monitoring. Our aim is to provide an introduction to this vibrant research area, starting from the physical principles at the basis of the methods and describing the main detector technologies and imaging tools, including their combination with conventional techniques from other disciplines, where appropriate. Then, we discuss critically some outstanding issues that affect a broad variety of applications, and the current state of the art in addressing them. Finally, we review several recent developments in the application of muography methods to specific use cases, without any pretence of exhaustiveness.
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