This contribution focuses on complex [Mo2(H)2(μ‐AdDipp2)2] (1) and tetrahydrofuran and pyridine adducts [Mo2(H)2(μ‐AdDipp2)2(L)2] (1⋅thf and 1⋅py), which contain a trans‐(H)Mo≣Mo(H) core (AdDipp2=HC(NDipp2)2; Dipp=2,6‐iPr2C6H3). Computational studies provide insights into the coordination and electronic characteristics of the central trans‐Mo2H2 unit of 1, with four‐coordinate, fourteen‐electron Mo atoms and ϵ‐agostic interactions with Dipp methyl groups. Small size C‐ and N‐donors give rise to related complexes 1⋅L but only one molecule of P‐donors, for example, PMe3, can bind to 1, causing one of the hydrides to form a three‐centered, two‐electron (3c‐2e) Mo‐H→Mo bond (2⋅PMe3). A DFT analysis of the terminal and bridging hydride coordination to the Mo≣Mo bond is also reported, along with reactivity studies of the Mo−H bonds of these complexes. Reactions investigated include oxidation of 1⋅thf by silver triflimidate, AgNTf2, to afford a monohydride [Mo2(μ‐H)(μ‐NTf2)(μ‐AdDipp2)2] (4), with an O,O’‐bridging triflimidate ligand.