The imprecise nature of psychiatric nosology restricts progress towards characterizing and treating mental health disorders. One issue is the ‘heterogeneity problem’: different causal mechanisms may relate to the same disorder, and multiple outcomes of interest can occur within one individual. Our review tackles this heterogeneity problem, providing considerations, concepts, and approaches for investigators examining human cognition and mental health. We highlight the difficulty of pure dimensional approaches due to ‘the curse of dimensionality’. Computationally, we consider supervised and unsupervised statistical approaches to identify putative subtypes within a population. However, we emphasize that subtype identification should be linked to a particular outcome or question. We conclude with novel hybrid approaches that can identify subtypes tied to outcomes, and may help advance precision diagnostic and treatment tools. The heterogeneity problem limits efforts to characterize typical and atypical cognitive phenomenon.Multidimensional approaches to overcome the heterogeneity problem are promising, but also limited by the curse of dimensionality.Identification of subpopulations through supervised and unsupervised methods offers an alternative approach toward characterizing heterogeneity.Supervised and unsupervised approaches toward characterizing heterogeneity are limited in that subpopulations are not tied to specific questions of interest.Hybrid methods that combine both supervised and unsupervised methods, such as FRF and SVA, are able to identify subpopulations tied to specific questions of interest (e.g., cognitive performance or treatment outcome), and may ultimately help refine psychiatric nosology.