To date, Artificial Intelligence systems for handwriting and drawing analysis have primarily targeted domains such as writer identification and sketch recognition. Conversely, the automatic characterization of graphomotor patterns as biomarkers of brain health is a relatively less explored research area. Despite its importance, the work done in this direction is limited and sporadic. This paper aims to provide a survey of related work to provide guidance to novice researchers and highlight relevant study contributions. The literature has been grouped into “visual analysis techniques” and “procedural analysis techniques”. Visual analysis techniques evaluate offline samples of a graphomotor response after completion. On the other hand, procedural analysis techniques focus on the dynamic processes involved in producing a graphomotor reaction. Since the primary goal of both families of strategies is to represent domain knowledge effectively, the paper also outlines the commonly employed handwriting representation and estimation methods presented in the literature and discusses their strengths and weaknesses. It also highlights the limitations of existing processes and the challenges commonly faced when designing such systems. High-level directions for further research conclude the paper.