Covalently closed circular RNAs (circRNAs) are produced by precursor mRNA back-splicing of exons of thousands of genes in eukaryotes. circRNAs are generally expressed at low levels and often exhibit cell-type-specific and tissue-specific patterns. Recent studies have shown that their biogenesis requires spliceosomal machinery and can be modulated by both cis complementary sequences and protein factors. The functions of most circRNAs remain largely unexplored, but known functions include sequestration of microRNAs or proteins, modulation of transcription and interference with splicing, and even translation to produce polypeptides. However, challenges exist at multiple levels to understanding of the regulation of circRNAs because of their circular conformation and sequence overlap with linear mRNA counterparts. In this review, we survey the recent progress on circRNA biogenesis and function and discuss technical obstacles in circRNA studies.