SiH has long been observed in the spectrum of our Sun and other cool stars. Computed line lists SiGHTLY for the main isotopologues of silicon monohydride, ^28^SiH, ^29^SiH, ^30^SiH and ^28^SiD are presented. These line lists consider rotation-vibration transitions within the ground X ^2^{Pi} electronic state as well as transitions to the low-lying A ^2^{Delta} and a ^4^{Sigma}^-^ states. Ab initio potential energy (PECs) and dipole moment curves (DMCs) along with spin-orbit and electronic-angular-momentum couplings between them are calculated using the MRCI level of theory with the MOLPRO package. The PEC for the ground X state is refined to available experimental data with a typical accuracy of around 0.01cm^-1^ or better. The ^28^SiH line list includes 11,785 rovibronic states and 1,724,841 transitions with associated Einstein-A coefficients for angular momentum J up to 82.5 and covering wavenumbers up to 31340cm^-1^ (>0.319um). Spectra are simulated using the new line list and comparisons made with various experimental spectra. These line lists are applicable up to temperatures of ~5000K, making them relevant to astrophysical objects such as exoplanetary atmospheres and cool stars and opening up the possibility of detection in the interstellar medium.