  Advanced LIGO and Advanced Virgo are expected to make the first direct
detections of gravitational waves (GW) in the next several years. Possible
types of GW emission include short-duration bursts, signals from the
coalescence of compact binaries consisting of neutron stars or black holes,
continuous radiation from fast-spinning neutron stars, and stochastic
background radiation of a primordial nature or resulting from the superposition
of a large number of individually unresolvable sources. We describe the
different approaches that have been developed to search for these different
types of signals. In this paper we focus on the GW detection methods
themselves; multi-messenger searches as well as further science enabled by
detections are dealt with in separate contributions to this volume.
