As the others have said, most carriers just roll you over to the next flight.
However as you know, sometimes things can get a little chaotic at the airport and gate agents can be snowed under, so it’s good, especially if you’re on a foreign trip, to have your backup plans ready to roll. That’s why I always stress including an alternate airport/route among your list of backups, because when things start going sideways, they go sideways fast, and having that alternate option in your back pocket can be the difference in a cot in the corner and your own bed.
A few years ago I was trying to get to Chicago. I’m at LAX, my flight had a light load, and I was sure I’ll be in F. Then came the announcement that all the remaining AA flights to Chicago were canceled because of high winds at ORD.
You can image the reaction to that announcement in the terminal-chaos, the agents were swamped.
My standing alternate airport/route for Chicago is to fly WN flight into Midway - Chicago‘s other airport., but I knew WN’s LAX/MDW flights were about to be inundated.
So I fell back to alternate airport/route plan B, bought a ticket to Vegas and then non-revved LAS to MDW on WN. I even won a little money on the machines at McCarran.
The main thing is I made it to Chicago in time for the graduation, as promised.
As the others have said, have back-ups/print-outs, don’t check bags, wear comfortable shoes and familiarize yourself with your departure terminal’s layout, just in case you have to sprint for that alternate plan B.