Genome editing methods have commonly relied on the initial introduction of double-stranded DNA breaks (DSBs), resulting in stochastic insertions, deletions, and translocations at the target genomic locus. To achieve gene correction, these methods typically require the introduction of exogenous DNA repair templates and low-efficiency homologous recombination processes. In this review, we describe alternative, mechanistically motivated strategies to perform chemistry on the genome of unmodified cells without introducing DSBs. One such strategy, base editing, uses chemical and biological insights to directly and permanently convert one target base pair to another. Despite its recent introduction, base editing has already enabled a number of new capabilities and applications in the genome editing community. We summarize these advances here and discuss the new possibilities that this method has unveiled, concluding with a brief analysis of future prospects for genome and transcriptome editing without double-stranded DNA cleavage.