Venationes should not be confused with execution by damnatio ad bestias, execution by being thrown to the beasts. A venator (plural venatores) was a specially trained beast hunter who was armed. (Those condemned to the beasts had no weapons and would sometimes be tied up as in the detail from the Zliten mosaic below (the mosaic is from the second century CE).
Imperial venatores were trained at the Ludus Matutinus, one of the four imperial gladiatorial training schools in Rome. (All were probably set up by Domitian, the last of the Flavian dynasty, the dynasty responsible for building the Colosseum.)
The first recorded venatio in Rome was held in 186 BCE, when Marcus Fulvius Nobilior had a hunt with lions and leopards as part of ten days of ludi (games) to celebrate his victory in the Aetolian War:
These [the Taurian Games] were followed by the ludi which M. Fulvius had vowed in the Aetolian war and were exhibited for ten days. 2 Many actors from Greece came to do him honour, and athletic contests were witnessed for the first time in Rome. The hunting of lions and panthers was a novel feature, and the whole spectacle presented almost as much splendour and variety as those of the present day. A shower of stones, lasting three days, fell at Picenum, and fire from the sky was said to have appeared in various places and singed many people’s garments.
Livy, From the Founding of the City 39.22
(Don’t worry about the shower of stones or fire from the sky in the passage above: such omens along with 2-headed cows and the like were apparently part and parcel of Roman life if Livy is to be believed. Julius Obsequens gathered them all from Livy and he’s well worth a read, especially for years when Rome has having troubles.)
Links and bibliography:
Requires Jstor access:
Christopher Epplett 2001 “The Capture of Animals by the Roman Military” Greece & Rome 48: 210-222. (This article talks about the role of the Roman army in catching animals for imperial era games.)