This chapter reviews various methods of detecting planetary companions to stars from an observational perspective, focusing on radial velocities, astrometry, direct imaging, transits, and gravitational microlensing. For each method, this chapter first derives or summarizes the basic observable phenomena that are used to infer the ex- istence of planetary companions, as well as the physical properties of the planets and host stars that can be derived from the measurement of these signals. This chapter then outlines the general experimental requirements to robustly detect the signals us- ing each method, by comparing their magnitude to the typical sources of measurement uncertainty. This chapter goes on to compare the various methods to each other by outlining the regions of planet and host star parameter space where each method is most sensitive, stressing the complementarity of the ensemble of the methods at our disposal. Finally, there is a brief review of the history of the young exoplanet field, from the first detections to current state-of-the-art surveys for rocky worlds.

60 pp, 12 figures. To appear as Chapter 59 of "Planets, Stars, and Stellar Systems" Editor-in-chief Terry Oswalt, volume editor Paul Kalas. v.2 corrects typo, adds citation