CRISPR-Cas is a bacterial defense system against phage infection and nucleic acid invasion. Class 2 type II CRISPR-Cas9 has also been widely used for genome engineering. Here, we review novel insights into the CRISPR class 2 type V enzymes, specifically Cpf1 and C2c1, which display different DNA-recognition and cleavage characteristics than those of Cas9, the best-characterized member of class 2. Recent structures of these ribonucleoprotein complexes that capture several stages of the endonuclease reaction have provided molecular details of recognition, unzipping and cleavage of the target DNA, allowing their comparison with Cas9. A detailed understanding of these mechanisms is crucial for improving these genome engineering tools and expanding the genomic space that can be targeted.