Admittedly you have to be at least 40 to remember the Dutch DAF car (it was absorbed into Volvo in the 1970s). It pioneered a transmission using a rubber pulley rather than individual gears.
The "rubber band" transmission later mutated into a steel belt and was tried in various small Fiats and Fords, but without much success. However, it is now catching on in the USA, of all places. In 2005 1% of cars in America had CVT (for Constantly Variable Transmission), By 2010 it was 7%, and according to the forecasting company IHS Automotive, it will hit 16% by 2016.