Competency-based medical education (CBME) addresses the accountability of postgraduate training programmes to graduate specialists capable of independent practice. We undertook a systematic review and narrative synthesis of the published CBME literature in anaesthesia training programmes to identify current practices and areas requiring further exploration. We grouped the 23 studies that met our inclusion criteria into the following categories: demonstrating outcomes of CBME, developing a consensus on an achievable CBME curriculum, CBME curriculum framework, design and implementation of workplace-based assessment (WBA) tools, trainee self-assessment, perceptions of trainees and supervisors on WBA tools, and technological solutions for assessment and feedback. Included studies reported variable success in reaching consensus in competency outcome frameworks for sequenced progression and limited research on approaches to curriculum delivery, whilst the majority of studies focused on workplace assessment. Studies supported the use of entrustment scales, where assessors make a judgement on the extent to which the trainee can manage a case independently. While evidence supported the reliability of WBA tools, and predicted the numbers needed for high-stakes decisions, areas of concern related to factors influencing the value WBA tools in promoting trainee learning, and variable perceptions of their value in making decisions on progression. Evidence on outcomes of CBME was limited to acquisition of specific competencies during training. The large number of unanswered questions and the dearth of studies across the core components of CBME suggest that we need a collaborative approach to create the evidence required to implement CBME wisely and cost effectively, to have positive impacts on patients, trainees, and healthcare systems.