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((PPr3)-Pr-i)(2) (1) loses a hydrogen molecule and the resulting unsaturated OsH4((PPr3)-Pr-i)(2) species coordinates 9-borabicycle[3.3.1]nonane (HBbn) and pinacol-borane (HBpin) to give the dihydrideborate derivatives OsH3{kappa(2)-H,H-(H2BR2)}((PPr3)-Pr-i)(2) (BR2 = Bbn (2), Bpin (3)). The bonding situation in these compounds and in the related osmium(II) derivative Os(Bcat){kappa(2)-H,H-(H(2)Bcat)}(CO)((PPr3)-Pr-i)(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((PPr3)-Pr-i)(2) also coordinates catecholborane, which initially affords OsH3{kappa(2)-H,H-(H(2)Bcat)}((PPr3)-Pr-i)(2) (5). In contrast to 2 and 3, complex 5 reacts with a second molecule of HBcat to give the elongated sigma-borane-{bis(elongated sigma)-dihydrideborate}-osmium(II) derivative OsH(eta(3)-H(2)Bcat)(eta(2)-HBcat)((PPr3)-Pr-i)(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 center dot NHMe2) and tert-butylamine-borane (H3B- (NH2Bu)-Bu-t) give OsH2(eta(2):eta(2)-H2BNR2)((PPr3)-Pr-i)(2) (NR2 = NMe2 (7), (NHBu)-Bu-t (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.