Mikey, it depends...
If you are asking about the trip home with a new swarm, I close the box and give them some kind of ventilation, especially in hot weather. Small holes punched in a cardboard box will work, or, if you are using a NUC or hive setup, a screened entrance is what works for me.
When the swarm gets home, you hope they do not abscond and continue to use your hive as their home.
Some people say you should feed them and trap them in their new home for three days. I'm assuming the rationale would be to let them make some comb and give the queen a chance to lay some eggs and let them hatch, which will usually anchor the bees to their new home.
I put a swarm on a few drawn combs and feed sugar syrup with a very small entrance opening to get them started. I also use a robbing screen. If you lock a new swarm in with a mated queen, they may stay and do well. If they have a virgin queen, she needs to fly to mate, and I don't like that delay before the hive can get started in earnest. So, you will hear a wide range of opinions on whether you should trap them inside for a few days before releasing them to gather nectar, or leave the entrance open. HTH
