The Hf-Mn system is of a long-time interest due to the intermetallic Laves phase HfMn2, a hydrogen storage material. Although this system has been experimentally investigated by several authors and critical reviews and thermodynamic modelling have been performed, there is still a lack of reliable information, particularly as the phase "HfMn" (sometimes labelled as "Hf3Mn2" or "Hf2Mn") is suspected to be oxygen stabilized. This work includes a thorough investigation of the Hf-Mn phase equilibria employing diffusion zones, thermal analysis, powder and single crystal X-ray analyses, analytical electron microscopy as well as physical property studies of the Laves phase (magnetic susceptibility, specific heat, electrical resistivity and mechanical properties). The phase near "HfMn" was shown (TEM, WDX electron microprobe data, X-ray single crystal analysis) to be an oxygen stabilized phase with the formula Hf3+xMn3_xO1_y (defect eta-W3Fe3C type). Properties such as magnetic susceptibility/magnetization; 2-300 K, specific heat (2-1100 K), electrical resistivity (2-300 K) classify HfMn2 as a metallic spin-fluctuation system with itinerant paramagnetism, originating from 3d states at Mn-sites and local moment paramagnetism of antisite Mn-atoms at Hf-sites. Mechanical properties (elastic moduli from density functional theory (DFT) and nanoindentation as well as hardness) group the Laves phase among rather hard and brittle intermetallics. DFT modeling revealed that Hf3+xMn3_x is thermodynamically unstable, but significant gains in enthalpy of formation arise from the inclusion of oxygen atoms, stabilizing the eta phase. All phase diagram and DFT data together with the former literature information were used for the thermodynamic CALPHAD-type modelling of the Hf-Mn system.