  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 man-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 reviewing several recent developments in the application of
muography methods to specific use cases, without any pretence of
exhaustiveness. We then describe the main detector technologies and imaging
methods, including their combination with conventional techniques from other
disciplines, where appropriate. Finally, we discuss critically some outstanding
issues that affect a broad variety of applications, and the current state of
the art in addressing them.
