Destructible, not destroyed. Like Battlefield.
There are only a small handful of destructible objects in Halo 4- the most commonly used are pallets and jersey barriers. Explosives can also be destroyed, as well as extraction crates, vehicles, grenades, and dominion turrets when they're deployed. However, these aren't really enough to make an entire environment with. There are also some tricks you can pull with the ricochet game type to get any object, including building blocks, to be destroyed in the game.