Objective assessment of an athlete's performance is of importance in elite sports to facilitate detailed analysis. The implementation of automated detection and recognition of sport-specific movements overcomes the limitations associated with manual performance analysis methods. The object of this study was to systematically review the literature on machine and deep learning for sport-specific movement recognition using inertial measurement unit (IMU) and, or computer vision data inputs. A search of multiple databases was undertaken. Included studies must have investigated a sport-specific movement and analysed via machine or deep learning methods for model development. A total of 52 studies met the inclusion and exclusion criteria. Data pre-processing, processing, model development and evaluation methods varied across the studies. Model development for movement recognition were predominantly undertaken using supervised classification approaches. A kernel form of the Support Vector Machine algorithm was used in 53% of IMU and 50% of vision-based studies. Twelve studies used a deep learning method as a form of Convolutional Neural Network algorithm and one study also adopted a Long Short Term Memory architecture in their model. The adaptation of experimental set-up, data pre-processing, and model development methods are best considered in relation to the characteristics of the targeted sports movement(s).