Resting-state functional MRI (rs-fMRI) is one of the most prevalent brain functional imaging modalities. Previous rs-fMRI studies have mainly focused on adults and elderly subjects. Recently, infant rs-fMRI studies have become an area of active research. After a decade of gap filling studies, many facets of the brain functional development from early infancy to toddler has been uncovered. However, infant rs-fMRI is still in its infancy. The image analysis tools for neonates and young infants can be quite different from those for adults. From data analysis to result interpretation, more questions and issues have been raised, and new hypotheses have been formed. With the anticipated availability of unprecedented high-resolution rs-fMRI and dedicated analysis pipelines from the Baby Connectome Project (BCP), it is important now to revisit previous findings and hypotheses, discuss and comment existing issues and problems, and make a "to-do-list" for the future studies. This review article aims to comprehensively review a decade of the findings, unveiling hidden jewels of the fields of developmental neuroscience and neuroimage computing. Emphases will be given to early infancy, particularly the first few years of life. In this review, an end-to-end summary, from infant rs-fMRI experimental design to data processing, and from the development of individual functional systems to large-scale brain functional networks, is provided. A comprehensive summary of the rs-fMRI findings in developmental patterns is highlighted. Furthermore, an extensive summary of the neurodevelopmental disorders and the effects of other hazardous factors is provided. Finally, future research trends focusing on emerging dynamic functional connectivity and state-of-the-art functional connectome analysis are summarized. In next decade, early infant rs-fMRI and developmental connectome study could be one of the shining research topics.