Translation as a decision-making process, associated with problem-solving activity, has been approached by a relatively long tradition of scholars and is still at the core of process-oriented research in translation studies. After reviewing the main contributions on this subject, the concepts of 'competence' and 'intrinsic motivation' are analysed from the perspective of both translation studies and psychology, particularly from the point of view of the Self-Determination Theory (SDT), as a theoretical background which could contribute to an extension of the conceptual framework of our discipline. After conducting a descriptive, correlational study of the three variables under analysis, the potential effect of competence and intrinsic motivation towards accomplishment on student translators' self-perceived problem-solving efficacy was gauged. Results showed that intrinsic motivation towards accomplishment and competence have the capability to predict problem-solving in a positive and significant way. Finally, in view of these findings, several strategies addressed to strengthen competence and intrinsic motivation towards accomplishment among translation trainees are suggested in order to help translator trainers to improve the learning and teaching process in University settings.