The CRISPR (clustered regularly interspaced short palindromic repeats)-Cas (CRISPR-associated) adaptive immune systems use small guide RNAs, the CRISPR RNAs (crRNAs), to mark foreign genetic material, e.g. viral nucleic acids, for degradation. Archaea and bacteria encode a large variety of Cas proteins that bind crRNA molecules and build active ribonucleoprotein surveillance complexes. The evolution of CRISPR-Cas systems has resulted in a diversification of cas genes and a classification of the systems into three types and additional subtypes characterized by distinct surveillance and interfering complexes. Recent crystallographic and biochemical advances have revealed detailed insights into the assembly and DNA/RNA targeting mechanisms of the various complexes. Here, we review our knowledge on the molecular mechanism involved in the DNA and RNA interference stages of type I (Cascade: CRISPR-associated complex for antiviral defense), type II (Cas9) and type III (Csm, Cmr) CRISPR-Cas systems. We further highlight recently reported structural and mechanistic themes shared among these systems.