Earthquake prediction is an area of research of great scientific and public fascination. The reason for this is not only that earthquakes can cause extremely large numbers of fatalities in a short time, but also because earthquakes can have a large social and economic impact on society. Earthquake prediction in the sense of making deterministic predictions about the place, time, and magnitude of earthquakes may very well be fundamentally impossible. However, based on a variety of data, earth scientists can make statements about the probability that earthquakes with a certain size will occur in a certain region over a specified time period. In this context one speaks of ''earthquake forecasting.'' A number of methods to achieve this are presented. However, it is not obvious how society should respond to these forecasts. It is shown that there is a fundamental dilemma for decision makers that statements of scientists concerning earthquake occurrence either contain very specific information but are very uncertain, or contain very general information but are very certain. Earthquake hazard can to a large extent be reduced by formulating and enforcing appropriate building codes. However, given the fact that the majority of the population that is threatened by earthquakes is living in the third world, it is clear that this cannot easily be realized. For these reasons, earthquake prediction is not only a scientific problem: it also has a complex political dimension.