Genetic syndromes associated with intellectual disability (ID) present with an increased prevalence of clinically significant autism characteristics. A greater severity of ID is often associated with a higher prevalence of autism characteristics in these syndromes (e.g., Down syndrome [DS], Prader-Willi syndrome [PWS]). However, the presence of ID alone falls short in explaining the distinct manifestation of these ‘syndromic’ forms of autism, wherein the behavioural characteristics differ in subtle and specific ways from non-syndromic autism. Social-cognitive theories offer a compelling account of the mechanistic differences that underlie the behaviour observed in non-syndromic autism. In autism research, eye-tracking technology has been widely used to investigate these social-cognitive abilities, including spontaneous gaze-following and implicit mentalising - reflecting more intuitive processes, which are not heavily dependent on intellectual functioning. Prior to this thesis, the utility of similar methods to study social cognition in people with ID was unclear, especially concerning the insight they could offer into the presence and profile of co-occurring autism characteristics. A systematic review of the literature demonstrated that eye-tracking is an accessible tool for people with ID, sensitive to detecting subtle social-cognitive processes. Furthermore, a meta-analysis yielded preliminary evidence indicating a significant correlation between reduced visual attention to socially salient regions of stimuli and a greater severity of autism characteristics in ID. Following this, two cross-syndrome eye-tracking studies were undertaken in DS, PWS, and non-syndromic autism. The focus on DS and PWS was primarily driven by a lack of research on social cognition in these syndromes, particularly concerning the co-occurrence of autism. The first study focused on characterising visual attention patterns and accuracy of spontaneous gaze-following. The second investigated a dissociation in explicit (a traditional verbal task) and implicit (an eye-tracking task) mentalising performance. In DS, the profile of spontaneous gaze-following and implicit mentalising abilities in some ways resembled that observed in non-syndromic autism, with greater difficulties associated with autism characteristics. In PWS, the profile of these abilities was somewhat distinct from DS and non-syndromic autism, and appeared attributable to the PWS phenotype, rather than the co-occurrence of autism per se. These insights provide evidence of how social-cognitive abilities may differently contribute to the manifestation of autism characteristics presented in these syndromes. A final study compared people with DS and PWS on an autism diagnostic observational assessment, revealing a similar presence and profile of autism characteristics in both syndromes. Notably, those with the highest level of autism-related needs could be distinguished from those with fewer needs, due to greater challenges with social-emotional reciprocity and non-verbal communication. Crucially, distinctions in the profiles of social-cognitive difficulties presented in each syndrome did not yield specific profiles of autism characteristics. Together, these findings challenge the universality and specificity of social-cognitive difficulties to autism, and underscore the complexity of autism heterogeneity across various conditions, including genetic syndromes. Such insights carry important clinical implications for understanding the manifestation of autism characteristics in genetic syndromes, while also contributing to a more inclusive, and comprehensive, conceptualisation of autism.