The discoveries of the first planets around a pulsar and around a star similar to our Sun have opened, after centuries of speculation, a new era in astronomy. The quest for other worlds has become reality. In this paper, the motivations for this search are presented. A comparative review is made of different techniques for their detection, with special attention paid to the planet parameters that can be derived from each method. The first discoveries and their astrophysical consequences are analysed. New questions and future projects beyond these first discoveries are reviewed, with special attention given to the search for life in extrasolar planetary systems. Finally, worldwide activities and the role of Europe are described.