Ponzi schemes are financial frauds that are pervasive throughout the world. Since they cause serious harm to society, it is of interest to study them so that they can be prevented. Typically, a Ponzi scheme is instigated by a promoter who promises above-average investment returns. He uses funds from the early investors to pay his later investors. These scams can occasionally last a long time, but they are ultimately unsustainable. This paper describes some well-known Ponzi schemes and identifies their common characteristics. We also review some of the approaches used to model Ponzi schemes.