When you request a refund, we process the item by the end of the day and often immediately. You can check the payment method that was refunded and the status of your refund in your "Billing History" under the "Account" section online.
Once we issue the refund, we typically see 2-10 days processing time by the financial institutions that handle this (which include Visa/Mastercard and the bank that issued the card). It varies by the kind of card/bank you use.
Why this delay? Honestly, there is no good reason, just know we issue them right away. Our company opinion is that it is ridiculous that banks can't process refunds immediately in today's age. These delays are common to all companies, including Amazon (see here for what they say on the matter).