Prokaryotic cells possess CRISPR-mediated adaptive immune systems that protect them from foreign genetic elements, such as invading viruses. A central element of this immune system is an RNA-guided surveillance complex capable of targeting non-self DNA or RNA for degradation in a sequence- and site-specific manner analogous to RNA interference. Although the complexes display considerable diversity in their composition and architecture, many basic mechanisms underlying target recognition and cleavage are highly conserved. Using cryoelectron microscopy (cryo-EM), we show that the binding of target double-stranded DNA (dsDNA)to a type I-F CRISPR system yersinia (Csy)surveillance complex leads to large quaternary and tertiary structural changes in the complex that are likely necessary in the pathway leading to target dsDNA degradation by a trans-acting helicase-nuclease. Comparison of the structure of the surveillance complex before and after dsDNA binding, or in complex with three virally encoded anti-CRISPR suppressors that inhibit dsDNA binding, reveals mechanistic details underlying target recognition and inhibition. Single-particle cryo-EM structures of a type I-F CRISPR surveillance complex before and after target dsDNA binding, as well as after inhibitor binding, demonstrate unique structural features for dsDNA recognition and a large global elongation of the complex, which may facilitate nuclease recruitment and subsequent target degradation.