Base editing is a genome editing strategy that induces specific single-nucleotide changes within genomic DNA. Two major DNA base editors, cytosine base editors and adenine base editors, that consist of a Cas9 protein linked to a deaminase enzyme that catalyzes targeted base conversion directed by a single-guide RNA have been developed. This strategy has been used widely for precise genome editing because, unlike CRISPR-Cas nuclease-based genome editing systems, this strategy does not create double-strand DNA breaks that often result in high levels of undesirable indels. However, recent papers have reported that DNA base editors can cause substantial off-target editing in both genomic DNA and RNA. The off-target editing described in these studies is primarily independent of guide RNA and arises from the promiscuous reactivity of the deaminase enzymes used in DNA base editors. In this Perspective, we discuss the development of DNA base editors, the guide RNA-independent off-target activity reported in recent studies, and strategies that improve the selectivity of DNA base editors.