This research project puts forward the joint application of experimental and computational techniques to understanding the interplay between magnetism (spins) and crystal structure (lattice) in quantum magnets and unconventional multiferroics. Both groups of materials are in the focus of present-day research devoted to strongly correlated electronic systems, exotic ground states, and unusual low-temperature properties. In these materials, the lattice is traditionally considered as a fixed and predefined parameter, although most lattices reveal a non-negligible response to the magnetic phenomena. Such mutual interplay of spins and lattice has important implications: for example, the formation of electric polarization in unconventional multiferroics. We will use both experimental, computational, and theoretical approaches to investigate the spin-lattice coupling in several representative materials featuring different chemical composition and structural elements. Our ultimate goals are the evaluation of the full spin-lattice Hamiltonian for specific magnetic systems, and the microscopic insight into the spin-lattice phenomena.