When you pour wine from its bottle into a nice glass container, this is an example of a time when you decant.
If it isn't, then re-cork the bottle and decant for sediment right before serving.
The lid of the oil bottle or jar has been designed so that the reeds can simply be pushed into the oil without the need to decant the oil to a separate container.
If it is very tannic, then decant and allow to aerate.
Many wine professionals suggest that you decant EVERY bottle of red wine you open.
They're wonderful for carrying a small decant of your favorite fragrance and popping in a purse or gym bag.