The infrared spectra of H-3(+) and D-3(+) Were first observed almost simult
aneously in 1980. Since then there has been extensive laboratory work on H-
3(+) and its D-isotopomers. In addition, the spectrum of H-3(+) has been ob
served in emission from the atmospheres of the giant planets Jupiter, Satur
n and Uranus, and probably from the supernova SN1987A, and recently in abso
rption in interstellar clouds. In this introductory paper, the assignment o
f the spectra and some of the characteristic features associated with the s
trong anharmonicity are discussed. As the convergence of the perturbation s
eries is poor, the large centrifugal effects are best calculated in a varia
tional type of approach, where the rotational energy in the Hamiltonian can
be treated essentially exactly. Ab initio calculations have steadily impro
ved over the years, and recent work has given completely theoretical vibrat
ion-rotation term values for the low vibrational states with an accuracy be
tter than 0.1 cm(-1) in almost all cases, adequate for most spectroscopic a
ssignment purposes.