  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.
