Cyclic-oligonucleotide-based anti-phage signalling systems (CBASS) are a family of defence systems against bacteriophages (hereafter phages) that share ancestry with the cGAS-STING innate immune pathway in animals. CBASS systems are composed of an oligonucleotide cyclase, which generates signalling cyclic oligonucleotides in response to phage infection, and an effector that is activated by the cyclic oligonucleotides and promotes cell death. Cell death occurs before phage replication is completed, therefore preventing the spread of phages to nearby cells. Here, we analysed 38,000 bacterial and archaeal genomes and identified more than 5,000 CBASS systems, which have diverse architectures with multiple signalling molecules, effectors and ancillary genes. We propose a classification system for CBASS that groups systems according to their operon organization, signalling molecules and effector function. Four major CBASS types were identified, sharing at least six effector subtypes that promote cell death by membrane impairment, DNA degradation or other means. We observed evidence of extensive gain and loss of CBASS systems, as well as shuffling of effector genes between systems. We expect that our classification and nomenclature scheme will guide future research in the developing CBASS field.