Although hyperthermophilic archaea arguably have a great need for efficient DNA repair, they lack members of several DNA repair protein families broadly conserved among bacteria and eukaryotes. Conversely, the putative DNA repair genes that do occur in these archaea often do not generate the expected phenotype when deleted. The prospect that hyperthermophilic archaea have some unique strategies for coping with DNA damage and replication errors has intellectual and technological appeal, but resolving this question will require alternative coping mechanisms to be proposed and tested experimentally. This review evaluates a combination of four enigmatic properties that distinguishes the hyperthermophilic archaea from all other organisms: DNA polymerase stalling at dU, apparent lack of conventional NER, lack of MutSL homologs, and apparent essentiality of homologous recombination proteins. Hypothetical damage-coping strategies that could explain this set of properties may provide new starting points for efforts to define how archaea differ from conventional models of DNA repair and replication fidelity.