A short perspective on a posteriori error control and adaptive discretizations

Error control by means of a posteriori error estimators or indica-tors and adaptive discretizations, such as adaptive mesh refinement, have emerged in the late seventies. Since then, numerous theoretical developments and improvements have been made, as well as the first attempts to introduce them into real-life industrial applications. The present introductory chapter provides an overview of the subject, highlights some of the achievements to date and discusses possible perspectives.