Pestiviruses are enveloped single-chain ribonucleic acid viruses with a positive polarity. Pestiviruses include the viruses of classical swine fever (hog cholera), Border disease of sheep, mucosal disease of cattle, and isolates obtained from wild animals, such as red deer (Cervus elaphus). Among ruminants, pestiviruses have developed a remarkable strategy for assuring their persistence. Through epigenetic transmission, they lead to the birth of asymptomatic carrier animals harbouring non-cytopathic variants, which become immunotolerant to the strain of virus present. The presence of a small number of asymptomatic carriers enables the virus to circulate within a herd by horizontal transmission, leading to the birth of a new generation of asymptomatic carriers.