When a fluid flows through different media (e.g. sand vs stone), the flow rates can change dramatically; we call this a heterogeneous problem. One may solve a heterogeneous problem using domain decomposition. In this talk, we analyze the optimized Schwarz method (OSM) for heterogeneous problems. To tackle the heterogeneity, we propose two possible, completely different approaches. First, we prove that if we choose our subdomains such that the jump in diffusivity is aligned with the subdomain interfaces, then the OSM converges at a rate that is independent of the fine grid parameter, h. Second, we prove that if we use a spectral coarse space (built from the eigenfunctions of subdomain D2N maps), we can obtain arbitrarily good convergence. Our theoretical results are supported by numerical experiments.