The CRISPR-associated protein 9 (Cas9) has been engineered as a precise gene editing tool to make double-strand breaks. CRISPR-associated protein 9 binds the folded guide RNA (gRNA) that serves as a binding scaffold to guide it to the target DNA duplex a RecA-like strand-displacement mechanism but without ATP binding or hydrolysis. The target search begins with the protospacer adjacent motif or PAM-interacting domain, recognizing it at the major groove of the duplex and melting its downstream duplex where an RNA-DNA heteroduplex is formed at nanomolar affinity. The rate-limiting step is the formation of an R-loop structure where the HNH domain inserts between the target heteroduplex and the displaced non-target DNA strand. Once the R-loop structure is formed, the non-target strand is rapidly cleaved by RuvC and ejected from the active site. This event is immediately followed by cleavage of the target DNA strand by the HNH domain and product release. Within CRISPR-associated protein 9, the HNH domain is inserted into the RuvC domain near the RuvC active site two linker loops that provide allosteric communication between the two active sites. Due to the high flexibility of these loops and active sites, biophysical techniques have been instrumental in characterizing the dynamics and mechanism of the CRISPR-associated protein 9 nucleases, aiding structural studies in the visualization of the complete active sites and relevant linker structures. Here, we review biochemical, structural, and biophysical studies on the underlying mechanism with emphasis on how CRISPR-associated protein 9 selects the target DNA duplex and rejects non-target sequences.