I'll answer for the US. As long as there's no official slot program, airlines can schedule however much they want to an airport, beyond what it should be capable of handling.
Now that doesn't mean ATC lets a free-for all happen. Hopefully, various traffic management units are on it and aware of how much demand is scheduled and already airborne into the airport/region/area that there's too much demand, and will implement various flow control programs to moderate the volume to what can be accepted into a specific sector(Certain airways can get super busy and require these types of actions), or airport. These control programs will either slow aircraft farther out from their destination, hold, or give small to longer delays on the ground, depending on how over scheduled or limitations of weather at the destination.
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Since the other part of the question wasn't there when I first answered, I'll answer now.
Slot controls vary heavily from airport to airport. In the US, LGA, LGB, DCA, SNA, and at times JFK are slot controlled, with a few others threatened to go to slots due to how many delays they impact the system(SFO, EWR, and ORD). How each airport deals with the slot allocation is different due to how they got slot controls. DCA is controlled partly through congress, LGA and SNA are restricted due to noise controls. In the US, once an airline gets a slot, often times it's considered transferable property, so airlines can sell them to each other if needed.
Now if a slot isn't used and goes back to the airport, the airport can put it up for bid, or allow applications for it, again depending on how their program is structured. AT DCA, some slots are transferable, some require an act of congress to change or modify, and some can only be used for certain routes or types of cities.