Circumbinary planets (CBPs) are planets that orbit around both stars of a binary system. This chapter traces the history of research on CBPs and provides an overview over the current knowledge about CBPs and their detection methods. After early speculations about CBPs, inspired by binary star systems and popularized by fictional works, their scientific exploration began with the identification of circumbinary dust disks and progressed to the detection and characterization of the current sample of CBPs. The major part of this chapter presents the detection methods for CBPs: eclipse timing variations from the light-travel-time effect and from dynamical interactions, transits, radial velocities, direct imaging, gravitational microlensing, and astrometry. Each of these methods is described with its strengths and limitations, and the main characteristics of the CBP systems found by them are outlined. The potential habitability of CBPs is considered, taking into account the unique environmental conditions created by orbiting a stellar binary. The importance of multimethod detection strategies is underscored, and future advancements from upcoming missions like PLATO are anticipated, promising to expand the understanding of these intriguing celestial bodies.