Change-point detection had its origins about sixty years ago in the work of Page, Shiryayev, and Lorden, whose focus concerned on-line detection of a change-point, i.e., an abrupt change in the distribution of a sequence of observations – representing a change in the quality of a continuous production process. More recently, motivation from a broad range of applications has lead to a variety of different problems. In this talk I will start with a historical review that leads to a number of applications and common features of different likelihood based formulations of present day research.