Current methods for broadband heteronuclear decoupling are reviewed from a historical perspective. The principal concern is that decoupling should be effective over a wide range of chemical shifts without undue radiofrequency heating of the sample, particularly when human patients are involved. Continuous-wave methods are the least efficient in this respect, followed by noise decoupling. Composite pulse schemes offer a more effective use of radiofrequency power, while adiabatic passage methods are the most efficient of all. Bi-level decoupling employs a low level of radiofrequency irradiation during the relaxation delay to maintain the nuclear Overhauser effect, with a higher level during signal acquisition in order to decouple over a wide frequency band. All decoupling sequences introduce cycling sidebands into the observed spectrum, and schemes are described to minimize the intensity of these artifacts. In part II, practical applications of decoupling methods are examined in the context of in vivo spectroscopy, where the improvements in sensitivity and resolution through broadband decoupling can be critical for solving clinical problems. Attention is focused on the regulatory limits on power deposition in these experiments. A tabulation of the existing work on decoupling in biological tissue is presented, mainly involving 31P and 13C spectroscopy in vivo or in vitro.