There are some people who believe Jesus Christ never actually lived. They think the early Christians made him up, and they’re known as mythicists. Almost no scholar agrees with them - you’d be hard-pressed to find a scholar, whether faithful or agnostic or atheist - who believes Jesus was made up. There are quite a few good reasons to believe Jesus was real, but perhaps the biggest is the crucifixion.
If you were starting a new religion circa 1st century CE, one thing you are not doing is making up a guy who gets nailed to a cross. Crucifixion was not just one of the worst ways to die - we get the modern word ‘excruciating’ from crucifixion - but it was also totally humiliating. It was a punishment usually reserved for slaves and low lives, and people were hung naked on the cross. The pain was one thing, but the shame of being on display like that, in a demeaning and vulnerable position (imagine a crow decides he wants your eye and your hands are nailed outstretched to your sides), would be unbelievable. The Romans themselves were kind of squeamish about it; Cicero condemned it, and very few Roman writers touch on the practice, despite the fact that the Romans were prolific crucifiers.
One of the final humiliations of crucifixion is that the body of the accused would often be left up on the cross well after death, serving as a warning to others who might be tempted to break the social order. No, if you were making up a religious figure who had to be martyred at the end of the story you’re not putting him on the cross. The cross was actually a symbol of mockery for early Christians - the oldest image we have of Jesus on the cross is graffiti found in a dorm for Imperial page boys in Rome, and it crudely depicts Jesus on the cross with the head of a donkey. A sketchy boy is standing before the cross and the words “Alexamenos worships his god” is scratched next to the cross.
No, it’s just about certain that Jesus lived. The question is what did he actually do, and this is what scholars try to figure out, to tease out of the Gospels and early traditions.
Jesus died on the cross on a Friday, and he was hurriedly removed from the instrument of his death before nightfall, when it would become the Sabbath. Jesus’ body was quickly entombed and left until Sunday, when Mary Magdalene came to find the tomb empty. (What was Jesus doing on Saturday? He was visiting Hell - I wrote about the Harrowing of Hell last year, and you can find it here ). That’s the story. Is it true?
In all four Gospels there’s a guy named Joseph of Arimathea (Monty Python fans may remember that he said you could find the Holy Grail in the Castle of Aaaargh), and he’s in charge of burying Jesus. Joseph is a rich man and a follower of Christ; in some Gospels he’s a member of the Sanhedrin who disagreed with what happened to Jesus. Joseph convinces Pontius Pilate to allow him to take the body of the dead rabble rouser and PIlate agrees; Joseph takes the corpse, wraps it in linen and myrrh, and puts it in his own personal tomb. It has to be done fast because the Sabbath is quickly approaching.
Jewish law prohibits leaving a body out overnight uncovered, and many people use this as proof that Jesus would have been buried immediately. The problem with that is the Jews, despite what Mel Gibson might say, were not the ones who killed Jesus. The Romans did. And it’s hard to imagine the Romans giving that much of a shit about Jewish custom.
One part of this story hinges on Pilate acquiescing to Joseph, and many historians call foul on that. They call foul on the depiction of Pilate in the Gospels in general; the guy who wanted to let Jesus go does not sound like the real guy. We know that Pilate was real, and that he was the governor of Judea at the time Jesus died. But we also know that he was a dick, and that there was a lot of tension between Pilate and the Jews, because he consistently did stuff that offended their religion. There are a number of such instances, attested to by contemporary historian Josephus, but one involves him bringing in imagery of Caesar under the cover of night and placing these idols all over the place, royally pissing off the Jews. They protested in front of his house for two days. Another story has another protest being broken up by Roman soldiers who beat many people to death with clubs. Pilate was not friendly with the Pharisees and he was not given to be giving a single damn about Jewish custom (Josephus mentions that the fact that Pilate brought the Caesar imagery in during the night indicates he knew that it was going to piss off the Jews).
The most likely thing to happen to Jesus’ body is that it would have just stayed on the cross for a couple of days. And while his body was up on that cross, it would have been fodder for scavengers - in fact, that was part of the point. There are numerous Roman writings attesting to the idea that they connected being crucified with being carrion. Here's a pretty evocative bit from Juvenal:
The vulture hurries from the dead cattle and dogs and crosses
To bring some of the carrion to her offspring.
One of the leading proponents of this theory is John Dominic Crossan, a Christian scholar who is quite sure that Christ ended up as scavenger food. In fact, he says that if the dogs didn’t get Jesus when he was on the cross (Jesus would have been easier pickings for crows at that point), they would have gotten him when his defiled body was eventually taken down and thrown in a pit. That’s what happened to victims of crucifixion - they were just tossed in a hole. Maybe - maybe! - they had some lime sprinkled on top, but they very plausibly were just left for the wild dogs to come and consume. It's interesting to note that out of all the bodies discovered from antiquity we have only ever found perhaps one or two that could be identified as victims of crucifixion - the fact that such bodies are never found indicates that crucified people were not given decent burials that would allow their bones to stick together and not, perhaps, get toted off by dog.
This is, of course, a major problem for Christianity. One of the core tenets of the faith is that Jesus was raised bodily from the dead, a feat that is much harder to accomplish when said body resides in the bellies of dogs. There are scholars who believe that Joseph of Arimathea was invented whole cloth to get around this problem - the Gospel authors come up with a guy who has the sway to get Jesus off the cross and away from the dogs, and make it plausible that his body can come back so that Thomas can stick his fingers in the hole in his side. A crucifixion was an embarrassment the Christians figured out how to use to their advantage, but being consumed by scavengers would have been harder to incorporate into their theology.
Recently scholars have begun to look at the possibility that the earliest Christians - remember, the Gospels were written decades after Jesus died - didn’t even believe in the tomb. There’s evidence, although scant and not well corroborated, that the earliest Christians believed that Jesus ascended to Heaven right from the cross, getting around the messiness of hungry crows and dogs.
There is one surprising piece of evidence in favor of Jesus being entombed - none of the earliest anti-Christian writers take issue with it. They attack the faith and the man from many, many angles, but they do not try to refute the idea that Jesus was buried. These people were living a century after Jesus, and we assume would have been familiar with the customs of crucifixion on some level, and yet they let this slide. Is it possible that one of the most underrated miracles of Jesus Christ was his ability to get a decent burial?
Note: speaking of early critics of Christianity, the earliest is a guy named Celsus. He is also perhaps the single most owned writer in history; Celsus wrote prolifically about how much Christianity sucks, but his writing now exists only as very extensive quotations in a refutation by the theologian Origen. Imagine that you write all this shit and the only way it survives is in a book wherein a guy goes point by point, line by line, saying how wrong you are? Literary fatality.