Cas12a (Cpf1) is a CRISPR-associated nuclease with broad utility for synthetic genome engineering, agricultural genomics, and biomedical applications. Although bacteria harboring CRISPR-Cas9 or CRISPR-Cas3 adaptive immune systems sometimes acquire mobile genetic elements encoding anti-CRISPR proteins that inhibit Cas9, Cas3, or the DNA-binding Cascade complex, no such inhibitors have been found for CRISPR-Cas12a. Here we use a comprehensive bioinformatic and experimental screening approach to identify three different inhibitors that block or diminish CRISPR-Cas12a-mediated genome editing in human cells. We also find a widespread connection between CRISPR self-targeting and inhibitor prevalence in prokaryotic genomes, suggesting a straightforward path to the discovery of many more anti-CRISPRs from the microbial world.