CRISPR–Cas12a (previously named Cpf1) is a prokaryotic deoxyribonuclease that can be programmed with an RNA guide to target complementary DNA sequences. Upon binding of the target DNA, Cas12a induces a nick in each of the target DNA strands, yielding a double-stranded DNA break. In addition to inducing cis-cleavage of the targeted DNA, target DNA binding induces trans-cleavage of non-target DNA. As such, Cas12a–RNA guide complexes can provide sequence-specific immunity against invading nucleic acids such as bacteriophages and plasmids. Akin to CRISPR–Cas9, Cas12a has been repurposed as a genetic tool for programmable genome editing and transcriptional control in both prokaryotic and eukaryotic cells. In addition, its trans-cleavage activity has been applied for high-sensitivity nucleic acid detection. Despite the demonstrated value of Cas12a for these applications, the exact molecular mechanisms of both cis- and trans-cleavage of DNA were not completely understood. Recent studies have revealed mechanistic details of Cas12a-mediates DNA cleavage: base pairing of the RNA guide and the target DNA induces major conformational changes in Cas12a. These conformational changes render Cas12a in a catalytically activated state in which it acts as deoxyribonuclease. This deoxyribonuclease activity mediates cis-cleavage of the displaced target DNA strand first, and the RNA guide-bound target DNA strand second. As Cas12a remains in the catalytically activated state after cis-cleavage, it subsequently demonstrates trans-cleavage of non-target DNA. Here, I review the mechanistic details of Cas12a-mediated cis- and trans-cleavage of DNA. In addition, I discuss how bacteriophage-derived anti-CRISPR proteins can inhibit Cas12a activity.