Is anyone familiar with the amounts of money that someone couple leave Belize or any other country with and re-enter the US with?

I've tried googling all sorts of things but with little luck.

All I've come up with is that it appears customs doesn't care as long as the amount isn't over 10K but what would the IRS say?

If someone were to make income on foreign soil - does the IRS have any ability to tax their citizens on that money?