Say someone bought Bitcoins from Coinbase and transferred them to their own wallet outside of Coinbase. They haven't sold them, so there's no taxes to pay and nothing to report to the IRS, right? How is the IRS going to know the difference between that situation, where they have done nothing wrong, and someone who sold them outside of Coinbase and didn't pay taxes on it? Are they just going to audit everyone over som…
How are they going to know the difference? For one, you can tell them. I don't know what the proper form for this would be, but I am sure an accountant can help out.
Scaremongering aside, I've found dealing with the IRS rather sane.
I would think that the IRS would treat a transfer of coins from a wallet you own to a wallet you do not own as a taxable event. They would take difference in value of the coins between when you acquired them and transferred them away, and if it is positive, would call it a profit.
On the other hand, if you declared that you owned both the source and destination wallet, I would imagine that the IRS would not treat this as a taxable event, in the same was as transferring USD between your checking and savings account is not a taxable event.
The IRS relies in a huge part on you self-reporting things. They do get a lot of info from the source (bank transaction records, 1099's, W2's). In many cases, the onus is on the taxpayer to tell the IRS the information that they need.
By default, the IRS takes self-reported information at face value and believes you. However, sometimes, they may decide to investigate. This is called an audit, and then the onus is on you to prove that what you provided is true.