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Pure rotational transitions of silicon monosulfide (28Si32S) and its rare isotopic species have been observed in their ground as well as vibrationally excited states by employing Fourier transform microwave (FTMW) spectroscopy of a supersonic molecular beam at centimetre wavelengths (13–37 GHz) and by using long-path absorption spectroscopy at millimetre and submillimetre wavelengths (127–925 GHz). The latter measurements include 91 transition frequencies for 28Si32S, 28Si33S, 28Si34S, 29Si32S and 30Si32S in υ = 0, as well as 5 lines for 28Si32S in υ = 1, with rotational quantum numbers J″≤ 52. The centimetre-wave measurements include more than 300 newly recorded lines. Together with previous data they result in almost 600 transitions (J″ = 0 and 1) from all twelve possible isotopic species, including 29Si36S and 30Si36S, which have fractional abundances of about 7 × 10−6 and 4.5 × 10−6, respectively. Rotational transitions were observed from υ = 0 for the least abundant isotopic species to as high as υ = 51 for the main species. Owing to the high spectral resolution of the FTMW spectrometer, hyperfine structure from the nuclear electric quadrupole moment of 33S was resolved for species containing this isotope, as was much smaller nuclear spin-rotation splitting for isotopic species involving 29Si. By combining the measurements here with previously published microwave and infrared data in one global fit, an improved set of spectroscopic parameters for SiS has been derived which include several terms describing the breakdown of the Born–Oppenheimer approximation. With this parameter set, highly accurate rotational frequencies for this important astronomical molecule can now be predicted well into the terahertz region. [ABSTRACT FROM AUTHOR]