A key task for customs workers is the interception of hazardous, illegal and counterfeit items in order to protect the health and safety of citizens. However, it is estimated that only a small fraction of cargo is inspected and an even smaller fraction of trafficked goods are detected. Today, the most widely used technology for scanning vehicles, ranging from vans and trucks to railcars, is γ ray and X-ray radiography. New technologies are required to overcome current technological shortcomings, such as the inability to detect the target material composition, the usage of harmful ionising radiation sources and the resultant low throughput. Cosmic ray tomography (CRT) is a promising technology for cargo screening. Cosmic ray muons have average energies of around 10,000 times larger than a typical X-ray and therefore can penetrate relatively large and dense materials. By analysing muon scattering, it is possible to identify materials hidden inside shielding that is too thick or deep for other imaging methods. CRT is also completely passive, exploiting naturally occurring secondary cosmic radiation, and is therefore safe for humans and animals. Contrary to conventional X-ray- or γ-ray-based imaging techniques, CRT also allows material differentiation and anomaly localisation within the cargo or vehicle through the provision of 3D images. This article reviews the current state-of-the-art technology in CRT, critically assessing the strengths and weaknesses of the method, and suggesting further directions for development.