Two types of risk are identified following the administration of a radiopharmaceutical to a patient: the risk to the patient, and the risk to critical groups exposed to the patient. The method for quantifying the risk to the patient is described in terms of estimating the effective dose. The main limitations in these estimates for adult and paediatric patients are uncertainties in the biokinetic data, and the assumption of a uniform distribution of activity in each organ. Effective doses from most nuclear medicine procedures will not exceed twice the annual dose from natural background radiation in the UK. Lack of human placental transfer data is now the main limitation to estimating fetal doses. The characteristics of two methods which can be used to derive the dose to critical groups exposed to nuclear medicine patients are reviewed. It is shown that studies using either method have indicated that the current recommendations in the UK for restricting the exposure of these groups and the recommendation recently proposed for restricting the exposure of pregnant members of staff are not appropriate. Revised recommendations for restricting the behaviour of patients administered iodine-131 should await the results of a current multicentre trial. The method to estimate the dose to a breast-fed infant from a mother administered a radiopharmaceutical is outlined, and the recently revised guidance for interrupting breast feeding is summarised. When a recommendation for controlling risk is to be derived from dosimetry data obtained from a number of individuals, an outstanding issue to be resolved is the value (e.g. 95% upper confidence limit) on which it should be based.