In this paper, the structural, magnetic and electronic properties of single-crystalline NiMnSb thin films grown by molecular beam epitaxy are presented. The growth process and surface morphology were studied by RHEED and STM. The structural quality of the films was investigated by EXAFS and HRTEM. For the optimized growth conditions, the expected NiMnSb C1b structure was obtained. Moreover, the most stable surface was found to be 4x1 reconstructed. The magnetic and electronic properties were studied by X-ray magnetic circular dichroïsm and spin-resolved x-ray photoemission spectroscopy experiments. The magnetization was observed to be essentially due to Mn, in agreement with theory. The surface was not found to be fully polarized but a polarization near 50% at room temperature was observed. Finally, the preparation of fully epitaxial NiMnSb/MgO/NiMnSb(001) trilayers is presented.