Norovirus, an ssRNA + virus of the family Caliciviridae, is a leading disease burden in humans worldwide, causing an estimated 600 million cases of acute gastroenteritis every year. Since the discovery of norovirus in the faeces of swine in Japan in the 1990s, swine norovirus has been reported in several countries on several continents. The identification of the human-associated GII.4 genotype in swine has raised questions about this animal species as a reservoir of norovirus with zoonotic potential, even if species-specific P-types are usually detected in swine. This review summarises the available data regarding the geographic distribution of norovirus in swine, the years of detection, the genotype characterisation, and the prevalence in specific production groups. Furthermore, we discuss the major bottlenecks for the detection and characterisation of swine noroviruses.