Imaging subsurface rock formations or geological objects like oil and gas reservoirs, mineral deposits, cavities or even magmatic plumbing systems under active volcanoes has been for many years a major quest of geoscientists. Since these subsurface objects cannot be observed directly, different indirect methods have been developed. These methods are all based on variations of certain physical properties of the subsurface materials that can be detected from the ground surface or from boreholes. To determine the density distribution, a new imaging technique using cosmic-ray muon detectors deployed in a borehole has been developed and a first prototype of a borehole muon detector successfully tested. In addition to providing a static image of the subsurface density in three dimensions (or three-dimensional tomography), borehole muography can also inform on the variations of density with time, which recently became of major importance with the injection of large volumes of fluids, mainly water and CO 2 , in porous subsurface reservoirs (e.g. aquifer storage and recovery, wastewater disposal, enhanced oil recovery and carbon sequestration). This raises several concerns about the risk of leakage and the mechanical integrity of the reservoirs. Determining the field scale induced displacement of fluids by geophysical methods like muography is thus a priority. This article is part of the Theo Murphy meeting issue ‘Cosmic-ray muography'.