After the Bretton Woods Accord came the Smithsonian Agreement in December of 1971. This agreement was similar to the Bretton Woods Accord, but allowed for a greater fluctuation band for the currencies. In 1972, the European community tried to move away from its dependency on the dollar. The European Joint Float was established by West Germany, France, Italy, the Netherlands, Belgium and Luxemburg. The agreement was similar to the Bretton Woods Accord, but allowed a greater range of fluctuation in the currency values
Both agreements made mistakes similar to the Bretton Woods Accord and in 1973 collapsed. The collapse of the Smithsonian agreement and the European Joint Float in 1973 signified the official switch to the free-floating system. This occurred by default as there were no new agreements to take their place. Governments were now free to peg their currencies, semi-peg or allow them to freely float. In 1978, the free-floating system was officially mandated.
In a final effort to gain independence from the dollar, Europe created the European Monetary System in July of 1978. Like all of the previous agreements, it failed in 1993.
The major currencies today move independently from other currencies. The currencies are traded by anyone who wishes. This has caused a recent influx of speculation by banks, hedge funds, brokerage houses and individuals. Central banks intervene on occasion to move or attempt to move currencies to their desired levels. The underlying factor that drives today's forex markets, however, is supply and demand. 
The onset of computers and technology in the 1980s accelerated the pace of extending the market continuum for cross-border capital movements through Asian, European and American time zones. Transactions in foreign exchange increased intensively from nearly billion a day in the 1980s, to more than $1.9 trillion a day two decades later.