Recently, there has been rising interest in replacing the linear (modular) cost function in combinatorial problems by a submodular cost function. This enhancement opens the door for powerful models, but at the same time leads to very hard optimization problems. Building on recent progress in submodular minimization with combinatorial constraints, and in online submodular minimization, this talk outlines routes for approximate online submodular minimization with combinatorial constraints. We address this scenario using the example of Minimum Cooperative Cut”, whose modular analogue, Minimum Cut, has been important in many applications.