It depends really.
Evolution doesn't just stop. Humans as they are now will evolve into something more suited to their natural environment, whatever that may be. If we classify all species after us that are our descendants as "humans", then we'll quite probably survive for the rest of time. We might spread ourselves out around the galaxy and have several divergent species, but as I said, these are ancestors that for the sake of this example we are calling "humans".
It is almost impossible to wipe out human life. We are far too well spread and biologically advanced to do so.
A nuclear war might wipe out a few hundred million. An asteroid might kill a few billion. But there's always some people left so the species continues. Even an out of control virus will have certain humans who are genetically resistant to it, just by the law of averages. Those will continue to survive and will pass the immunity on to their children.
People talk about the food chain, but humans will adapt to survive. It might mean that we will start eating more and more insects as our primary protein. It might mean that we start cannibalising each other. It matters not, we will survive in numbers somewhere.
Even if the worst possible climate change event happens, we will still survive somewhere. There's literally no realistic scenario that could cause a species wide extinction across the entire planet outside of the planet itself exploding and that would need another planet size object to hit it. Maybe we could poison the atmosphere but as it would be a slow event, when it started killing the elderly and the like the human species would adapt, either by changing behaviour or by invention.
I'm all for ideas here, as I can't think of a single thing that could possibly kill us all.
Our descendants will adapt to their new surroundings and rediscover the science that brought to where we are now. The future of "humanity" is definitely in space, whether that be us as a species or somebody quite like us, it is where we will end up when all said and done