Structured sequence processing tasks inform us about statistical learning abilities that are relevant to many areas of cognition, including language. Despite the ubiquity of these abilities across different tasks and cognitive domains, recent research in humans has demonstrated that these cognitive capacities do not represent a single, domain-general system, but are subject to modality-specific and stimulus-specific constraints. Sequence processing studies in nonhuman primates have provided initial insights into the evolution of these abilities. However, few studies have examined similarities and/or differences in sequence learning across sensory modalities. We review how behavioural and neuroimaging experiments assess sequence processing abilities across sensory modalities, and how these tasks could be implemented in nonhuman primates to better understand the evolution of these cognitive systems.