There is a common misconception that the corpses of fallen gladiators were treated poorly—dragged out by hooks like diseased animal corpses, for instance. This and many other indignities were inflicted on the damnati, condemned criminals who were tortured and killed in the arena. These events took place at midday, the meridianum spectaculum, and it is described vividly by Seneca (Ep. 7.3-5). Some were just forced to fight each other to the death, while others were forced to participate in gruesome pageants of violent myths, were set against large beasts, etc. If you can imagine it, the Romans probably did it to damnati. For a society that did not have prisons, this was an important route for the disposal of undesirable members. Seneca has no question that it was just punishment, but is somewhat disturbed at just how much the crowds loved it. The public mutilation of undesirable members of society is in no way isolated to the Romans. See, for instance, Caesar's vivid description of the Gauls creating huge wicker effigies and stuffing them with live criminals before setting them on fire (BG 6.16).

But gladiators were not damnati. In Roman society, a gladiator's death was his last and greatest achievement, the ultimate attainment of Roman virtus. Gladiatorial events were very clearly separated from the slaughter of animals or of criminals, even though they occurred in the same space and both involved mortal violence. Contrary to what is commonly repeated, not every gladiator was killed on an outing. In fact, less than 50% of gladiators were killed over their career by the 2nd century CE, and the number was even lower before that. Gladiators were an expensive commodity, like a modern stallion, and they were pampered as such. Upon their death, when it did come, they were carefully collected from the sand and placed on a stretcher or cart. Dead gladiators departed the arena from the same place as slain criminals, but this had nothing to do with their status: the Gate of Death, the Porta Libitinaria, was the liminal progression of all who fell in the arena, no matter of species or status, and it was presided over by the obscure goddess Libitina, associated with funerals and the passage from life to death. Many later accounts of gladiatorial deaths involve a pageant of figures dressed as Charon, Hades, etc, but these are much later Christian accounts and are very much muddled with the antics of the midday spectacles. We aren't sure what happened to the corpses after they left the arena, but we have references to a place called the spoliarium, where, based on the name, gladiators had their equipment removed after a fight. It is presumed that the corpses would also be tended to here, probably by staff of the school and with all due reverence.

Like other members of Roman society, gladiator burials after they departed the arena were determined by the status, connections, and preparations of the deceased. Many belonged to burial clubs (collectives which ensured that members were properly interred when the time came). We have some scattered but good evidence that the gladiator schools themselves took care of the burial of valued gladiators. So a Roman epitaph (CIL 6.10171) records that a guy named Claudius Agathocles, who was a physician at the Ludus Matutinus (school) in Rome, paid for the burial (and epitaph) for himself and also a few colleagues: a lanista, a curator of the spoliarum, and a gladiator, a retiarius. That a gladiator was included among three non-gladiator staff of the school suggests a great deal of respect. There was a hierarchy among the ludus and of course some gladiators were much more important than others, however.

Another route we sometimes see is the erection of a polyandria by the editor of a gladiatorial spectacle. This was a sort of mass grave, but nicely appointed, which would house multiple slain gladiators. The point of such a monument was, cynically, both to advertise the virtus of the slain and their skill in the spectacle, but also to advertise the editor who put them out there. Like many tombs in the ancient world, then, it was self-serving in its expense.

For those gladiators who were not fortunate enough to be buried, we know very little. Many gladiators left behind epitaphs, but many more assuredly did not. Whether they wound up in the same disposal flowcharts as other impoverished dead is unknown (dumped in pits outside the city, e.g.). I personally tend to doubt it, and suggest that even the lowliest received some sort of dignified burial via their school, their trainers, or their peers...if they fought well and did not embarrass themselves.

The go-to source for this topic is Kyle, Spectacles of Death in Ancient Rome (Routledge 1998). See also his more broad Sport and Spectacle in the Ancient World (Wiley Blackwell 2014/2015). For important visual evidence of the clear separate of gladiatorial fights from animal hunts and the killing of undesirables, see the Zliten mosaic.