The Caliciviridae are viruses with a positive-sense, single-stranded RNA genome that is packaged into an icosahedral, environmentally stable protein capsid. The family contains five genera (Norovirus, Nebovirus, Sapovirus, Lagovirus, and Vesivirus) that infect vertebrates including amphibians, reptiles, birds, and mammals. The RNA-dependent RNA polymerase (RdRp) replicates the genome of RNA viruses and can speed up evolution due to its error-prone nature. Studying calicivirus RdRps in the context of genuine virus replication is often hampered by a lack of suitable model systems. Enteric caliciviruses and RHDV in particular are notoriously difficult to propagate in cell culture; therefore, molecular studies of replication mechanisms are challenging. Nevertheless, research on recombinant proteins has revealed several unexpected characteristics of calicivirus RdRps. For example, the RdRps of RHDV and related lagoviruses possess the ability to expose a hydrophobic motif, to rearrange Golgi membranes, and to copy RNA at unusually high temperatures. This review is focused on the structural dynamics, biochemical properties, kinetics, and putative interaction partners of these RdRps. In addition, we discuss the possible existence of a conserved but as yet undescribed structural element that is shared amongst the RdRps of all caliciviruses.