Bryaxis is a large genus, with over 400 described species and subspecies (Hlaváč 2008), of small beetles belonging to the group known as the Pselaphinae, a subgroup of the Staphylinidae. In older references, you'll see the pselaphines referred to as a separate family Pselaphidae from the staphylinids, but most authors now include it in the latter as it has become clear that the pselaphines are not only related to the staphylinids but nested well within them. It is not so surprising that this was not immediately recognised: your average staphylinid looks something like this:
Bryaxis species are mostly found living in leaf litter, where they are predators of other micro-arthropods such as springtails. If you look at the top photo, you will be see two appendages with paddle-shaped endings attached to the head just behind the antennae. These are the maxillary palps, often enlarged in pselaphines (sometimes ridiculously so). Glands on the inside of the palp 'paddle' produce a sticky secretion, and the palps are used to grab the prey when hunting. The process of prey capture in Bryaxis puncticollis was illustrated by Schomann et al. (2008):
As befits a large genus, Bryaxis has a truly headache-inducing taxonomic history, summarised by Besuchet (1966). The genus was first named by Kugelann in 1794. Kugelann's work can't have been that widely publicised, however, because in 1817 Leach gave the name Bryaxis to a different genus of pselaphine. Most subsequent authors used Bryaxis in the sense of Leach, and included Kugelann's original Bryaxis in the genus Bythinus, until this was corrected by Raffray in 1904. Raffray treated Bythinus as a junior synonym of Kugelann's Bryaxis, and placed Leach's 'Bryaxis' under the name Rybaxis. Even so, some European authors persisted in using Leach's Bryaxis.
It wasn't until the 1950s and 1960s that the usage of Bryaxis became stabilised, but there was one further wrinkle to the story. When Raffray identified Bythinus as a synonym of the true Bryaxis, he separated out a few previous Bythinus species as a new genus Bolbobythus. However, one of those was the type species of Bythinus. So, as finally laid out by Besuchet (1966): what had been called 'Bolbobythus' was really Bythinus, 'Bythinus' was really Bryaxis, and 'Bryaxis' was really Rybaxis! What could be simpler?
Besuchet, C. 1966. Bryaxis Kugelann, 1794 and Bythinus Leach 1817 (Insecta, Coleoptera): proposed addition to the Official List in their original sense. Bulletin of Zoological Nomenclature 23 (2-3): 114-116.
Hlaváč, P. 2008. A new cavernicolous species of the genus Bryaxis (Coleoptera: Staphylinidae: Pselaphinae) from the island of Mljet. Natura Croatica 17 (1): 1-8.
Schomann, A., K. Afflerbach & O. Betz. 2008. Predatory behaviour of some Central European pselaphine beetles (Coleoptera: Staphylinidae: Pselaphinae) with descriptions of relevant morphological features of their heads. European Journal of Entomology 105: 889-907.