Neurodevelopmental disorders (NDD) are impairments of the growth and development of the brain and/or central nervous system. In the light of clinical findings on early diagnosis of NDD and prompted by recent advances in hardware and software technologies, several researchers tried to introduce automatic systems to analyse the baby’s movement, even in cribs. Traditional technologies for automatic baby motion analysis leverage contact sensors. Alternatively, remotely acquired video data (e.g., RGB or depth) can be used, with or without active/passive markers positioned on the body. Markerless approaches are easier to set up and maintain (without any human intervention) and they work well on non-collaborative users, making them the most suitable technologies for clinical applications involving children. On the other hand, they require complex computational strategies for extracting knowledge from data, and then, they strongly depend on advances in computer vision and machine learning, which are among the most expanding areas of research. As a consequence, also markerless video-based analysis of movements in children for NDD has been rapidly expanding but, to the best of our knowledge, there is not yet a survey paper providing a broad overview of how recent scientific developments impacted it. This paper tries to fill this gap and it lists specifically designed data acquisition tools and publicly available datasets as well. Besides, it gives a glimpse of the most promising techniques in computer vision, machine learning and pattern recognition which could be profitably exploited for children motion analysis in videos.