This chapter, originally written as a consequence of the terrorist attacks of September 11, 2001, provides an elementary, everyday introduction to the concepts of risk and insurance. Conceptually, risk has two dimensions: a potential loss, and the chance of that loss being realized. People can, however, transfer risk to insurance companies against the payment of so-called premiums. In practice, however, one needs accurate assessments of both losses and probabilities to judge whether premiums are appropriate. For many risks, this poses little problem (e.g., life insurance); however, it is difficult to assess risks of many other kinds of events such as acts of terrorism. It is emphasized, that through evolution and learning, people are able to handle many of the common risks that they face in life. But when people lack experience (e.g., new technologies, threats of terrorism), risk can only be assessed through imagination. Not surprisingly, insurance companies demand high prices when risks are poorly understood. In particular, the cost of insurance against possible acts of terrorism soared after September 11. How should people approach risk after the events of that day? Clearly, the world needs to protect itself from the acts of terrorists and other disturbed individuals. However, it is also important to address the root causes of such antisocial movements. It is, therefore, suggested that programs addressed at combatting ignorance, prejudice, and social inequalities may be more effective premiums for reducing the risk of terrosrtism than has been recognized to date.