Clipless pedals help keep your feet in position on the pedals. Cycling shoes are necessary for using clipless pedals.
Toe clips on pedals also help keep your feet in position and can be used with other kinds of shoes, although they, too, work best with cycling shoes.
There are many cyclists, such as 10 Wheels, who use neither and are able to ride a ton of miles without difficulty.
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Bacchetta Giro A20, RANS V-Rex, RANS Screamer