Interplay between multiple degrees of freedom — spin, orbital, and lattice — is a promising way to achieve novel phases of matter and functional materials. Development of recent electronic structure tools, such as density-functional theory (DFT) or dynamical mean-field theory (DMFT), has enabled ab-initio study of such phenomena in real materials, and here I will talk about a couple of such examples where electron correlations and spin-orbit coupling take an essential role. In the first example, a deficient spinel chalcogenide GaV_4S_8, I will show that spin-states of V_4 clusters and the crystal structure are closely coupled to each other based on our cluster DMFT calculation results employing molecular orbital bases. In the second example, I will talk about a possible solid-state realization of the Haldane model in a Fe-based honeycomb layered honeycomb compound from the cooperation of spin-orbit coupling and the on-site Coulomb interaction within the Fe d-orbitals.