The downside is the risk that you fry your chip because you don't know what you are doing. (I fried my first CPU, an i5-2500k, due to a freak motherboard voltage compensation event on startup, but it was ultimately my fault for using too high a LLC setting that was completely unnecessary) Also you decrease the life of the chip (although marginally if not an extreme overclock) by running it at higher temps and voltages.
Think about it, if there were no downsides, why would it just not come clocked higher from the factory?
You can run the high clock all the time, but modern CPUs are designed to clock down at idle, running cooler and saving power. That's why when people overclock, they are actually just raising the turbo/boost clock that the CPU clocks up to under load.