New gene editing tools like CRISPR-Cas9 enable precision genome engineering within cell lines, primary cells, and model organisms, with some formulations now entering the clinic. "Precision" applies to various aspects of gene editing, and can be tailored for each application. Here we review recent advances in four types of precision in gene editing: 1) increased DNA cutting precision (e.g., on-target:off-target nuclease specificity), 2) increased on-target knock-in of sequence variants and transgenes (e.g., increased homology-directed repair), 3) increased transcriptional control of edited genes, and 4) increased specificity in delivery to a specific cell or tissue. Design of next-generation gene and cell therapies will likely exploit a combination of these advances.