Proton radiography and tomography have long promised benefit for proton therapy. Their first suggestion was in the early 1960s and the first published proton radiographs and CT images appeared in the late 1960s and 1970s, respectively. More than just providing anatomical images, proton transmission imaging provides the potential for the more accurate estimation of stopping-power ratio inside a patient and hence improved treatment planning and verification. With the recent explosion in growth of clinical proton therapy facilities, the time is perhaps ripe for the imaging modality to come to the fore. Yet many technical challenges remain to be solved before proton CT scanners become commonplace in the clinic. Research and development in this field is currently more active than at any time with several prototype designs emerging. This review introduces the principles of proton radiography and tomography, their historical developments, the raft of modern prototype systems and the primary design issues.