During the last 20 years, TeV astronomy has turned from a fledgling field, with only a handful of sources, into a fully-developed astronomy discipline, broadening our knowledge on a variety of types of TeV gamma-ray sources. This progress has been mainly achieved due to the currently operating instruments: imaging atmospheric Cherenkov telescopes, surface arrays and water Cherenkov detectors. Moreover, we are at the brink of a next generation of instruments, with a considerable leap in performance parameters. This review summarizes the current status of the TeV astronomy instrumentation, mainly focusing on the comparison of the different types of instruments and analysis challenges, as well as providing an outlook into the future installations. The capabilities and limitations of different techniques of observations of TeV gamma rays are discussed, as well as synergies to other bands and messengers.