Circular RNAs (circRNAs) are emerging as novel regulators of gene expression in various biological processes. CircRNAs regulate gene expression by interacting with cellular regulators such as microRNAs and RNA binding proteins (RBPs) to regulate downstream gene expression. The accumulation of high-throughput RNA–protein interaction data revealed the interaction of RBPs with the coding and noncoding RNAs, including recently discovered circRNAs. RBPs are a large family of proteins known to play a critical role in gene expression by modulating RNA splicing, nuclear export, mRNA stability, localization, and translation. However, the interaction of RBPs with circRNAs and their implications on circRNA biogenesis and function has been emerging in the last few years. Recent studies suggest that circRNA interaction with target proteins modulates the interaction of the protein with downstream target mRNAs or proteins. This review outlines the emerging mechanisms of circRNA–protein interactions and their functional role in cell physiology.