If you move but keep your citizenship, you must still report your worldwide income. You may be eligible for a Foreign Earned Income Exclusion and a Foreign Tax Credit for what tax is paid to the foreign country... but ALL US CITIZENS must report and maybe pay.
The rules on reporting foreign bank accounts still apply.
If you give up your citizenship, a U.S. citizenship could owe an EXIT TAX.
if their average tax per year for the five years before expatriating exceeds $161,000
or they have a net worth of $2 million or more. It works as if you have sold all your assets
and will be taxed on profit that exceeds an exemption of nearly $700k.