Ambulation is defined by duration, distance traversed, number and size of directional changes and the interval separating successive movement episodes; more complex measures of ambulation can be created by aggregating these features. This review article of published findings defines random changes in direction during movement as “movement path tortuosity”, and relates tortuosity to the understanding of cognitive impairments of persons of all ages. Path tortuosity is quantified by subjecting tracking data to fractal analysis, specifically Fractal Dimension (Fractal D), which ranges from a value of 1 when the movement path is perfectly straight to a value of 2 when the movement path is random, resembling the “drunkard’s walk”. The review elucidates the mathematical assumptions underlying Fractal D, its use in the analysis of movements of free ranging animals, and its application to the study of cognitive impairment and the prediction of falls in older adults. We conclude Fractal D offers a reliable, valid, sensitive and easily interpreted real-time longitudinal measure of unrestricted movement path tortuosity unaffected by mobility aid use.