The use of hadron beams, especially proton beams, in cancer radiotherapy has expanded rapidly in the past two decades. To fully realize the advantages of hadron therapy over traditional x-ray and gamma-ray therapy requires accurate positioning of the Bragg peak throughout the tumor being treated. A half century ago, suggestions had already been made to use protons themselves to develop images of tumors and surrounding tissue, to be used for treatment planning. The recent global expansion of hadron therapy, coupled with modern advances in computation and particle detection, has led several collaborations around the world to develop prototype detector systems and associated reconstruction codes for proton computed tomography (pCT), as well as more simple proton radiography, with the ultimate intent to use such systems in clinical treatment planning and verification. Recent imaging results of phantoms in hospital proton beams are encouraging, but many technical and programmatic challenges remain to be overcome before pCT scanners will be introduced into clinics. This review introduces hadron therapy and the perceived advantages of pCT and proton radiography for treatment planning, reviews its historical development, and discusses the physics related to proton imaging, the associated experimental and computation issues, the technologies used to attack the problem, contemporary efforts in detector and computational development, and the current status and outlook.