At one point Japan's Nikkei 225 index was down 7%, but recovered some of those losses to close 4.7% lower.
London, Frankfurt and Paris all fell sharply when they opened on Tuesday with new losses of up to 3%. In the US overnight the Dow lost 4.6%.
The falls follow some good years for investors. In 2017 the Dow was up 25%, helped by a resurgent economy.
Strong profits and low interest rates also underpinned the positive investment climate.