Visible light LEDs, due to their numerous advantages, are expected to become the dominant indoor lighting technology. These lights can also be switched ON/OFF at high frequency, enabling their additional use for wireless communication and indoor positioning. In this article, visible LED light--based indoor positioning systems are surveyed and classified into two broad categories based on the receiver structure. The basic principle and architecture of each design category, along with various position computation algorithms, are discussed and compared. Finally, several new research, implementation, commercialization, and standardization challenges are identified and highlighted for this relatively novel and interesting indoor localization technology.