Utilizing novel synchrotron-based 161Dy nuclear resonant scattering (NRS) studies, the present thesis provides insight into the hyperfine interactions and molecular vibrational properties of single-molecule magnets (SMMs). Such molecular magnetic materials show a slow relaxation of the magnetization due to their intrinsic magnetic bistability. In addition, SMMs display magnetic hysteresis effects of purely molecular origin and are therefore considered promising candidates for technological applications in spintronics, molecular electronics or in future quantum computing. In particular, the lanthanide Dy is of pivotal importance due to its inherently large magnetic moment and high magnetic anisotropy. To contribute to the understanding of magnetic relaxation dynamics in Dy-based SMMs, the present work aims to establish two related synchrotron-based NRS techniques. Both research tools are based on the Mössbauer effect, and exploit the 25.65 keV nuclear resonance of the Mössbauer isotope 161Dy. 161Dy nuclear forward scattering is demonstrated as a suitable tool to explore the static and dynamic hyperfine interactions of molecular compounds and in particular of SMMs. In addition, the conducted study establishes 161Dy nuclear inelastic scattering as a unique experimental method giving access to information on acoustic and optical phonons, the understanding of which is of key relevance for the research and development of SMMs.