  The purpose of this chapter is to provide an overview of the exciting field
of black hole quasi-normal modes and its capabilities to test general
relativity in the 21st century. After motivating this line of research, we
provide a qualitative introduction to the concept of quasi-normal modes and
outline black hole perturbation theory. With the perturbation equations at
hand, we discuss common methods to compute the quasi-normal mode spectrum and
compare the advantages and disadvantages of each approach. We also provide an
overview of possible deviations from general relativity and how they modify the
quasi-normal mode spectrum of black holes from a theoretical point of view. We
then review the rapidly evolving status of currently operating gravitational
wave observatories and experimental results. The chapter concludes with a
discussion of open problems and promising outlooks to theoretical and
experimental developments. Central pieces that make this chapter particularly
interesting, also for advanced readers, are comprehensive tables providing a
detailed overview of the status of techniques to compute quasi-normal modes and
methods to describe quasi-normal modes of rotating black holes beyond general
relativity.
