The bicycle derailleur—the part which allows a cyclist to switch gears—was developed in the late 1800s, but didn't become common racing equipment until the late '30s. Since then, advancements have come quickly, with some sort of new development coming roughly once every other year.
Current high-end systems feature 11 gears on the rear wheel and two or three up front. Shifting is either mechanical or electronic, and while electronic shifting is still mostly a high-end option, the technology is beginning to trickle down. On a first bike, however, mechanical is probably still the way to go.