We review some recent investigations on prototypical SiC-based interfaces, as obtained from first-principles molecular dynamics. We discuss the interface with vacuum, and the role played by surface reconstruction in SiC homoepitaxy, and adatom diffusion. Then we move to the description of a buried, highly mismatched semiconductor interface, the one which occurs between SiC and Si, its natural substrate for growth: in this case, the mechanism governing the creation of a network of dislocations at the SiC/Si interface is presented, along with a microscopic description of the dislocation core. Finally, we describe a template solid/liquid interface, water on SiC: based on the predicted structure of SiC surfaces covered with water molecules, we propose (i) a way of nanopatterning cubic SiC(001) for the attachment of biomolecules and (ii) experiments to reveal the local geometry of adsorbed water.