The velvet crab (Necora puber), also known as the velvet swimming crab or devil crab, is a species of crab from the North-East Atlantic and the Mediterranean.

The velvet crab was first formally described in 1767 by Carl Linnaeus in the second part of the first volume of the twelfth edition of his definitive work Systema Naturae. Linnaeus gave it the name Cancer puber; at the time, all crabs were classified indiscriminately into the genus Cancer. Necora puber is commonly known as the "velvet crab", the "velvet swimming crab", and the "devil crab", the latter due to its aggressive behaviour and bright red eyes. In the Scottish fishing industry, they are sometimes known just as "velvets", and other less pervasive common names include the "velvet fiddler crab" the "lady crab", and the "Kerry witch".

Linnaeus provided a very brief Latin description ‒ "vague and unsatisfactory", according to Lipke Holthuis. In fact, the identity of Linnaeus's crab in unclear, as no type material was assigned and the description given seems to more closely resemble Polybius corrugatus. Since Linnaeus' initial 1767 description, the velvet crab has been reclassified four times: first into Portunus by Fabricius in 1798, a classification which stood until 1958, when it was transferred to Macropipus by Holthuis and Gottlieb. In 1981 Manning and Holthuis moved it to Liocarcinus, and six years later Holthuis reclassified the species into an entirely new genus, Necora, of which the velvet crab is the only species. This classification still stands. The genus name Necora comes from the local word for the crabs in Galicia. Several species names described by other taxonomists have since been synonymised with N. puber.

Recent phylogenetic studies of the Portunoidea and related groups have considered Necora several times in their research. Necora is usually grouped with members of the genera Bathynectes, Liocarcinus, Macropipus, Polybius, and Thia.

A phylogenetic study published in Frontiers in Zoology in 2022 used both maximum parsimony and bayesian inference and analysed morphological characteristics placed Necora puber in a monophyletic Carcinidae clade. Of the surveyed species, Necora was sister to a Macropipus rugosus / Thia grouping. However, a study using nuclear DNA from 2009 placed Thia sister to a clade that includes Necora, but also species from Macropipus, Liocarcinus, Polybius, and Bathynectes. The authors of the 2009 study noted that the conventional classifications of the Portunoidea and Canceroidea have recently been challenged, and some morphological traits – especially those of the carapace and the chelae – can be affected by convergent evolution. The 2016 study kept Necora in the Polybiidae. A yet earlier (2001) study using mitochondrial DNA of 46 species paired Necora with Bathynectes maravigna, close to Macropipus tuberculatus and Thia.

In the British Isles, velvet crabs are found from Orkney around Scotland, England, Wales, and Ireland. They also live in the nearby German Bight and in parts of the West Frisian Islands.

Velvet crabs have a dark, flattened carapace which ranges from black to brown in colour and is usually around 6.5 cm long and up to 10 cm across, weighing up to 250 grams. The carapace is pubescent with short yellowish hairs providing a velvety texture. Tubercles are scattered across the upper surface, with a higher concentration towards the front. The frontal part of the crab's underside has some tubercles as well and is densely hairy. The front of the carapace is mostly straight and bends slightly inwards at the centre line; the front edge bears seven to ten tooth-like indentations. The claw-bearing legs (the chelipeds) also have short hairs and are of equally short length. The "wrist" is armed with a spine on its outer side.

Velvet crabs are "very common".