The TRIATOM program suite calculates energy levels, wavefunctions, and where appropriate, dipole transition moments and spectra, for rotating and vibrating triatomic molecules. Potential energy, and where necessary, dipole surfaces must be provided. The programs use an ''act (within the Born-Oppenheimer approximation) Hamiltonian, offer a choice of several body-fixed, internal coordinate systems based on two distances and an included angle and employ basis function expansions of orthogonal polynomials. The calculations are variational, and rotational excitation is treated using an efficient two-step algorithm. Constituent programs are TRIATOM which solves the vibrational problem and also performs the first step for rotationally excited systems. SELECT which optionally preselects basis functions for TRIATOM. ROTLEVD which performs the second step for rotationally excited states. DIPOLE computes either line or band transition intensities. SPECTRA uses the data generated by the other programs to give simulated absorption or emission spectra.