With advances in data-driven machine learning research, a wide variety of prediction models have been proposed to capture spatio-temporal features for the analysis of video streams. Recognising actions and detecting action transitions within an input video are challenging but necessary tasks for applications that require real-time human-machine interaction. By reviewing a large body of recent related work in the literature, we thoroughly analyse, explain and compare action segmentation methods and provide details on the feature extraction and learning strategies that are used on most state-of-the-art methods. We cover the impact of the performance of object detection and tracking techniques on human action segmentation methodologies. We investigate the application of such models to real-world scenarios and discuss several limitations and key research directions towards improving interpretability, generalisation, optimisation and deployment.