First, you have to fill out personal taxes every year for foreign income, regardless of whether you live in the US or not. All income globally is treated in the eyes of the IRS as income.
Second, you have to declare FBAR if you hold foreign accounts of over $10,000.
Third, you have to "open your books" for any foreign corporations you are the director (or have ownership) of. Check IRS forms 5471 and 5472.
Yaaa! Land of the free!
Source: American with a business in the UK, lived and worked in the UK. Not a lawyer, or an accountant.