CRISPR-mediated DNA base editors, which include cytosine base editors (CBEs) and adenine base editors (ABEs), are promising tools that can induce point mutations at desired sites in a targeted manner to correct or disrupt gene expression. Their high editing efficiency, coupled with their ability to generate a targeted mutation without generating a DNA double-strand break (DSB) or requiring a donor DNA template, suggests that DNA base editors will be useful for treating genetic diseases, among other applications. However, this hope has recently been challenged by the discovery of DNA base editor shortcomings, including off-target DNA editing, the generation of bystander mutations, and promiscuous deamination effects in both DNA and RNA, which arise from the main DNA base editor constituents, a Cas nuclease variant and a deaminase. In this review, we summarize information about the DNA base editors that have been developed to date, introduce their associated potential challenges, and describe current efforts to minimize or mitigate those issues of DNA base editors.