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Molecular spectroscopy plays a vital role in the field of astronomy and astrophysics. It furnishes the useful and important details on the study of physical conditions of the astrophysical sources such as relative abundances, effective temperature, magnetic field strength and velocity of the mass motion, etc. Many diatomic molecules have been identified in the spectra of variety of astrophysical sources. Studies of molecular lines can be used to refine models since they form in higher layer of the atmosphere. Many unidentified lines especially found in the solar spectrum may be of molecular origin, and may belong to the identified and unidentified species. In view of their application in sunspots, with the help of known or already identified molecules, dissociation equilibrium calculations coupled with center to limb equivalent width and profile calculations may help in model testing. The molecular lines can also be used for magnetic field measurements in the sunspots.