The motorized bicycle concept has been around since the late 1800's. Taking the basic bicycle frame and adding a motor to do some or all of the pedaling for you made the biking experience easier. Initially inventors were crazy about the motorized bicycle and in the 1800's there were several patents for a variety of motors. Most of these motors wouldn't be looked at again until the early 1990's, about a hundred years later.
The motorized bicycle is considered environmentally friendly, which may add to their popularity. They are sometimes called light electric vehicles and may be listed on your license as such. They're different from motorcycles since motorcycles don't have pedals to fall back on to power the vehicle. Mopeds have pedals but there may be legal restrictions on using the pedals so check with your local DMV or Motor Vehicle Authority.
The U.S. is seeing a spike in demand for the motorized bicycle. Countries where bicycles are already popular had nearly as many motorized bicycles as other vehicles in the mid 90's. Electric bicycles are the most popular and China has been selling them by the millions since the early part of this century.
While the electric motorized bicycle is the most popular around the world, there is a motorized bicycle or two that uses the internal combustion engine to get going. Bolt on bike motors saw a boom of popularity in the 60's. A variety of manufacturers, including Sears, produced the motors which continued to sell into the 70's. Cleaner and more efficient engines are making these motors popular again.
Electric motorized bicycles are almost overwhelming in the varieties of motors and batteries that are available. Newer batteries are longer lasting and lighter giving the rider a drive range of around 25-30 miles (40-50 km). There is a distinction in the source of power an electric motorized bicycle has available. Power on demand is usually located in the handle bars. Pedelec is sometimes called power assist, since you'll have to pedal to control the motor.
The motorized bicycle won't be outselling conventional vehicles, in the U.S. at least, any time soon, but they are popular. Check your area for clubs and hobbyist groups. As a hobby motorized bikes are extremely popular and allow individuals to share modification information. Some unique modifications include the steam powered motorized bikes or solar powered bikes.