I've had clients who hid money offshore and didn't pay tax on it. They were evading taxes on purpose. I didn't like those guys and dropped them as clients.
However, most of my clients have had “inadvertent” issues.
Let's see there was my green card holder from Australia with an apartment back there and bank accounts, which he didn't think counted. Then there was my Irish friend who owned land, a house and had rental income and bank accounts, which he didn't think counted.
So, while the tax rules are very complicated, this one is very, very simple. If you are a Green Card Holder or a US citizen, all of your income from anywhere in the world is taxed in the US. That's it, US taxation on worldwide income.
In the past, my Australian friend and Irish buddy went on their merry way and just ignored the overseas stuff.
NO MORE. The risks of getting caught are very high and the cost is very high.
Bottom line is that the US has gotten serious about this stuff. The data systems and US power now enables them to actually find the accounts. The US has improved its data collection, entered into many agreements with foreign governments, and it has required new reporting (FATCA).
So you should expect that if you have offshore stuff you have not included on your return it will now be found.
The unreported stuff is a felony. That is ugly.
If you think the tax bill was high, wait until you get the lawyer's fee to keep you out of jail (hopefully) along with the tax you should have paid, penalties and interest (just double it for a rule of thumb).