The hydrogenation and dehydrogenation of benzene on Pt(111) is examined from first principles using DFTGGA cluster calculations. The reactive benzene species is adsorbed at the hollow site. The addition of the first H-atom has a barrier of 74 kJ/mol and is +11 kJ/mol endothermic. There are five different pathways available for the addition of the second hydrogen atom. The dominant path is the one that forms the 1,3dihydrobenzene intermediate. This reaction has a barrier of 72 kJ/mol and is +34 kJ/mol endothermic. The hydrogenation of the C6H7* intermediate can also form 1,3-cyclohexadiene, which has a barrier of 91 kJ/mol and is +38 kJ/mol endothermic, or 1,4-cyclohexadiene, which has a barrier of 115 kJ/mol and is +36 kJ/mol endothermic. Two types of hydrogenation mechanisms were distinguished. The "three-centered" mechanism was found to be more favorable than the "slip" mechanism. The dehydrogenation of benzene to phenyl is +76 kJ/mol endothermic. Therefore benzene dehydrogenation is neither thermodynamically nor kinetically a favorable reaction path. Dehydrogenation to o-benzyne is +14 kJ/mol endothermic relative to benzene. The calculated barriers are in qualitative and quantitative agreement with experimental data.