the miner that includes your transaction in a block. the first miner to do so gets the transaction fee, hence you can pay a high fee and guarantee it is included or pay a standard fee and it will probavly be included in the next 2-3 blocks or if you are not in a rush you can send it with no fee (providing it meets a few other criteria) and it will get processed usually within 24 hours.

the miners are the people that produce new bitcoins and secure the network.