We describe the recent discovery of promising new Ge-based magnetic semiconductors and heterostructures using combinatorial molecular-beam epitaxy for the science and applications of spintronics. We discuss key experimental considerations for implementing combinatorial synthesis and characterization, and highlight important findings in epitaxial films of (100) Ge doped by Co and Mn, specifically the ternary epitaxial phase-diagram, and the novel magnetic and electrical-transport phenomena. We illustrate the natural "marriage" between the controlled synthesis and combinatorial approach, and demonstrate the usefulness of the approach for studying complex epitaxial process.