This paper focuses on acquisition and processing methods in positron emission tomography/computed tomography (PET/CT) for radiotherapy (RT) applications. The recent technological evolutions of PET/CT systems are described. Particular emphasis is dedicated to the tools needed for the patient positioning and immobilization, to be used in PET/CT studies as well as during RT treatment sessions. The effect of organ and lesion motion due to patient's respiration on PET/CT imaging is discussed. Breathing protocols proposed to minimize PET/CT spatial mismatches in relation to respiratory movements are illustrated. The respiratory gated (RG) 4D-PET/CT techniques, developed to measure and compensate for organ and lesion motion, are then introduced. Finally a description is provided of different acquisition and data processing techniques, implemented with the aim at improving: i) image quality and quantitative accuracy of PET images, and ii) target volume definition and treatment planning in RT, by using specific and personalised motion information.