CRISPR (clustered regularly interspaced short palindromic repeats)-based immune systems are essentially modular with three primary functions: the excision and integration of new spacers, the processing of CRISPR transcripts to yield mature CRISPR RNAs (crRNAs), and the targeting and cleavage of foreign nucleic acid. The primary target appears to be the DNA of foreign genetic elements, but the CRISPR/Cmr system that is widespread amongst archaea also specifically targets and cleaves RNA in vitro. The archaeal CRISPR systems tend to be both diverse and complex. Here we examine evidence for exchange of functional modules between archaeal systems that is likely to contribute to their diversity, particularly of their nucleic acid targeting and cleavage functions. The molecular constraints that limit such exchange are considered. We also summarize mechanisms underlying the dynamic nature of CRISPR loci and the evidence for intergenomic exchange of CRISPR systems.