In medical decision making, statistical modeling plays a prominent role. The likelihood theory provides a generally applicable method to estimate and test parameters in a statistical model. The method goes back to one of the most famous statisticians from history, Sir Ronald A. Fisher, who worked on the method between 1912 and 1922. Most statistical methods make use of likelihood methods. This entry begins by explaining the likelihood function and then maximum likelihood estimation. Next, it discusses the properties of maximum likelihood estimation. This entry closes with a discussion of the application of likelihood methods for testing a null hypothesis.