The formation and Atoms in Molecules (AIM) analysis of osmium(IV) and osmium(II) complexes containing dihydrideborate groups and primary aminoborane ligands are reported. Complex OsH6(P iPr3)2 (1) loses a hydrogen molecule and the resulting unsaturated OsH4(P iPr3)2 species coordinates 9-borabicycle[3.3.1]nonane (HBbn) and pinacolborane (HBpin) to give the dihydrideborate derivatives OsH3{κ2- H, H-(H2BR2)}(P iPr3)2 (BR2 = Bbn (2), Bpin (3)). The bonding situation in these compounds and in the related osmium(II) derivative Os(Bcat){κ2- H, H-(H2Bcat)}(CO)(P iPr3)2 (4) (HBcat = catecholborane) has been analyzed by the AIM method. The Laplacian distributions in the Os-H-B plane exhibit a four-membered cyclic topology possessing two Os-H and two B-H bond critical points associated with one OsHHB ring critical point, which resembles that found for B2H6. The tetrahydride OsH4(P iPr3)2 also coordinates catecholborane, which initially affords OsH3{κ2- H, H-(H2Bcat)}(P iPr3)2 (5). In contrast to 2 and 3, complex 5 reacts with a second molecule of HBcat to give the elongated σ-borane-{bis(elongated σ) -dihydrideborate}-osmium(II) derivative OsH(η3-H2Bcat)(η2-HBcat)(P iPr3)2 (6). Complexes 5 and 6 have been also analyzed via the AIM method. Complex 5 displays the same topology as complexes 2-4. However, the OsH2B unit of 6 shows, besides the Os-H and B-H bond critical points, an additional Os-B bond critical point, which is associated with a bond path running between these atoms. This double triangular topology is completed with the respective ring critical points. Reactions of 1 with dimethylamine-borane (H3B·NHMe2) and tert-butylamine-borane (H3B·NH2tBu) give OsH2(η2:η2-H2BNR2)(P iPr3)2 (NR2 = NMe2 (7), NH tBu (8)). The AIM analyses of 7 and 8 also reveal the occurrence of an Os-B bond critical point associated with a bond path running between those atoms. However, neither Os-H bond critical points nor bond paths are observed in the latter species.