While research on autism spectrum disorder (ASD) has been growing, not enough research has been conducted to understand the impact of autistic traits and the broader autism phenotype (BAP), especially on the sleep quality and well-being of university students. The focus of this paper is to review the existing research on this topic and identify the key areas of interest for future research, presented in the form of a narrative review. While the review identifies the need for research on the topic, it also identifies other factors such as gender, age, culture, and internet and smartphone use that may have an impact on the relationship between autistic traits, sleep quality and well-being in university students. The review also identified the importance of using a larger sample size, appropriate measures, especially for quantifying autistic traits, and an appropriate analysis strategy involving a multivariate analysis.