There is a remarkable redox chemistry of higher oxidation state M(IV)-M(VI) polypyridyl complexes of Ru and Os. They are accessible by proton loss and formation of oxo or nitrido ligands, examples being cis-[RuIV(bpy)2(py)(O)]2+ (RuIV=O2+, bpy=2,2'-bipyridine, and py=pyridine) and trans-[OsVI(tpy)(Cl)2(N)]+ (tpy=2,2':6',2' '-terpyridine). Metal-oxo or metal-nitrido multiple bonding stabilizes the higher oxidation states and greatly influences reactivity. O-atom transfer, hydride transfer, epoxidation, C-H insertion, and proton-coupled electron-transfer mechanisms have been identified in the oxidation of organics by RuIV=O2+. The Ru-O multiple bond inhibits electron transfer and promotes complex mechanisms. Both O atoms can be used for O-atom transfer by trans-[RuVI(tpy)(O)2(S)]2+ (S=CH3CN or H2O). Four-electron, four-proton oxidation of cis,cis-[(bpy)2(H2O)RuIII-O-RuIII(H2O)(bpy)2]4+ occurs to give cis,cis-[(bpy)2(O)RuV-O-RuV(O)(bpy)2]4+ which rapidly evolves O2. Oxidation of NH3 in trans-[OsII(tpy)(Cl)2(NH3)] gives trans-[OsVI(tpy)(Cl)2(N)]+ through a series of one-electron intermediates. It and related nitrido complexes undergo formal N- transfer analogous to O-atom transfer by RuIV=O2+. With secondary amines, the products are the hydrazido complexes, cis- and trans-[OsV(L3)(Cl)2(NNR2)]+ (L3=tpy or tpm and NR2-=morpholide, piperidide, or diethylamide). Reactions with aryl thiols and secondary phosphines give the analogous adducts cis- and trans-[OsIV(tpy)(Cl)2(NS(H)(C6H4Me))]+ and fac-[OsIV(Tp)(Cl)2(NP(H)(Et2))]. In dry CH3CN, all have an extensive multiple oxidation state chemistry based on couples from Os(VI/V) to Os(III/II). In acidic solution, the OsIV adducts are protonated, e.g., trans-[OsIV(tpy)(Cl)2(N(H)N(CH2)4O)]+, and undergo proton-coupled electron transfer to quinone to give OsV, e.g., trans-[OsV(tpy)(Cl)2(NN(CH2)4O)]+ and hydroquinone. These reactions occur with giant H/D kinetic isotope effects of up to 421 based on O-H, N-H, S-H, or P-H bonds. Reaction with azide ion has provided the first example of the terminal N4(2-) ligand in mer-[OsIV(bpy)(Cl)3(NalphaNbetaNgammaNdelta)]-. With CN-, the adduct mer-[OsIV(bpy)(Cl)3(NCN)]- has an extensive, reversible redox chemistry and undergoes NCN(2-) transfer to PPh3 and olefins. Coordination to Os also promotes ligand-based reactivity. The sulfoximido complex trans-[OsIV(tpy)(Cl)2(NS(O)-p-C6H4Me)] undergoes loss of O2 with added acid and O-atom transfer to trans-stilbene and PPh3. There is a reversible two-electron/two-proton, ligand-based acetonitrilo/imino couple in cis-[OsIV(tpy)(NCCH3)(Cl)(p-NSC6H4Me)]+. It undergoes reversible reactions with aldehydes and ketones to give the corresponding alcohols.