This review synthesized current literature of behavioral and cognitive studies targeting reward processing in autism spectrum disorder (ASD). The National Institute of Mental Health's Research Domain Criteria (RDoC) Positive Valence System (PVS) domain was used as an overarching framework. The objectives were to determine which component operations of reward processing may be atypical in ASD and consequently postulate a heuristic model of reward processing in ASD that could be evaluated with future research. 34 studies were identified from the Embase, PubMed, PsycINFO, and Web of Science databases and included in the review using guidelines from the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (also known as PRISMA guidelines). The extant literature suggested potential relationships between social symptoms of ASD and PVS sub-constructs of reward anticipation, probabilistic and reinforcement learning, reward prediction error, reward (probability), delay, and effort as well as between restricted and repetitive behaviors and interests (RRBIs) and PVS-sub constructs of initial response to reward, reward anticipation, reward (probability), delay, and effort. However, these findings are limited by a sparse and mixed literature for some sub-constructs. We put forward a developmentally informed heuristic model that posits how these component reward processes may be implicated in early ASD behaviors as well as later emerging and more intransigent symptoms. Future research is needed to comprehensively evaluate the proposed model.