A systematic review of the literature on statistical and machine learning schemes for identifying symptoms of developmental stuttering from audio recordings is reported. Twenty-seven papers met the quality standards that were set. Comparison of results across studies was not possible because training and testing data, model architecture and feature inputs varied across studies. The limitations that were identified for comparison across studies included: no indication of application for the work, data were selected for training and testing models in ways that could lead to biases, studies used different datasets and attempted to locate different symptom types, feature inputs were reported in different ways and there was no standard way of reporting performance statistics. Recommendations were made about how these problems can be addressed in future work on this topic.