They can be opened by damaging them, for instance with the whip.
The empty Chest remains after being looted, and can be carried. However, as a heavy object, it does not go far when thrown and cannot be taken through the level exit with you.
When opened, Chests will contain a random assortment of 3-4 large and small jewels, but not diamonds.
When opened, each Chest normally produces from 6 to 8 random large jewels, and never contain any small ones. There have been a couple cases where Vaults have a higher value than the one possible with 16 ghosted diamonds, leading to think that sometimes Vault Chests might contain more than 8 large gems.
There is a small chance that Chests may be booby-trapped to release a primed bomb when opened, and usually contain only one or two small jewels. There is no way to tell if a Chest is rigged before you open it.
Trap bombs explode with the same power as regular Bombs, but have shorter fuses.
As an explosion deals 10 points of damage, it is usually fatal to be caught in one. For this reason, it is always advisable to be prepared to escape a potential fiery death when opening Chests.
There have been a small amount of cases where a chest contains two bombs. This might indicate that every gem has a very small chance of spawning as a bomb.