Objective: Infant sleep development is a highly dynamic process occurring in parallel to and in interaction with cognitive and physical growth. This narrative review aims to summarize and discuss recent literature and provide an overview of the relation between infant sleep and cognitive development as well as physical growth. Methods: We conducted online literature search using MEDLINE, Embase, and Cochrane Library databases. We considered original research on humans published in the English language from January 2005 to December 2015. Search terms included "sleep" AND "infant" AND "cognition" OR "memory" OR "executive functioning", OR "growth" OR "obesity" OR "growth hormone" OR "stunting", and combinations thereof. Results: Ten studies on infant sleep and cognition were included in this review. Overall, findings indicated a positive association between sleep, memory, language, executive function, and overall cognitive development in typically developing infants and young children. An additional 20 studies support the positive role of infant sleep in physical growth, with the current literature focusing largely on weight gain and obesity rather than healthy growth. Existing evidence in both the domains is mainly based on cross-sectional designs, on association studies, and on parental reports. In contrast, there were limited studies on longitudinal sleep trajectories and intervention effects, or studies have not used more objective sleep measures such as actigraphy and polysomnography. Conclusion: The reviewed studies support a critical and positive role of infant sleep in cognition and physical growth. Future studies should consider key environmental and parental confounders, include a combination of more objective (actigraphy) and subjective measures (sleep diaries and questionnaires), and move towards longitudinal trajectory designs of infant sleep and development.