Black Hole Quasinormal Modes in the Era of LIGO

After a long wait, gravitational wave astronomy has finally begun. Binary black hole mergers are being detected by LIGO and Virgo, and theorists are starting to receive a wealth of data to be analyzed. At this point, we can at long last begin to test alternative theories of gravity and different models of compact objects. One powerful tool to do this is the perturbative analysis of background spacetimes. The objective of this brief review is to introduce the notion and analysis of black hole quasinormal modes, starting from the linear perturbation theory and including a brief discussion of numerical methods and astrophysical implications in the gravitational wave signals recently detected. With these basic ingredients, more sophisticated analyses and applications are possible.