The most recent example of a broadly-levied surtax in the United States was one imposed to help finance the Vietnam War during the Lyndon B. Johnson administration. It essentially consisted of calculating one's ordinary federal income tax liability and then adding another 10% to it -- the amount of the surtax.
As the U.S. Income Tax Code at that time was an extreme example of progressive taxation, the surtax was much higher on those with higher incomes, as a 10% surtax imposed on a tax rate of 20% would result in an overall rate of 22%, while the same surtax imposed on a rate of 50% would result in an overall rate of 55%.
Some anti-war protesters refused to pay this tax, stating that while they were not anarchists and understood the need for and positive role played by government in many areas, they wanted none of their tax money going to a war that they felt was immoral. The surtax was repealed well before the war ended in Vietnam.
Surtaxes can be imposed on other taxes. They are usually imposed on the grounds of moral justification; they only affect persons who are already paying taxes rather than extending taxation to new areas or persons who are not previously being taxed.
A surtax of 4.3 percent was recently proposed on incomes over $500,000 by Congress to alleviate the alterations to the Alternative Minimum Tax code in the United States.
In 1929, Supertax (which had been introduced in the Finance Act 1909 at the rate of 6 old pence in the pound (2.5%) on incomes over 5000 per year) was renamed Sur-tax. By 1934, the rate was variable from 1 shilling to 7 shillings and sixpence in the pound (5% to 37.5%).