The adsorbed magnetic molecules with tunable spin states have drawn wide attention for their immense potential in the emerging fields of molecular spintronics and quantum computing. One of the key issues toward their application is the efficient controlling of their spin state. This review briefly summarizes the recent progress in the field of molecular spin state manipulation on surfaces. We focus on the molecular spins originated from the unpaired electrons of which the Kondo effect and spin excitation can be detected by scanning tunneling microscopy and spectroscopy (STM and STS). Studies of the molecular spin-carriers in three categories are overviewed, i.e., the ones solely composed of main group elements, the ones comprising 3d-metals, and the ones comprising 4f-metals. Several frequently used strategies for tuning molecular spin state are exemplified, including chemical reactions, reversible atomic/molecular chemisorption, and STM-tip manipulations. The summary of the successful case studies of molecular spin state manipulation may not only facilitate the fundamental understanding of molecular magnetism and spintronics but also inspire the design of the molecule-based spintronic devices and materials.