Diagrammatic Monte Carlo (DMC) is a powerful method which has proven to work for many different systems. It makes use of diagrammatic expansions of Green's functions and a Metropolis sampling algorithm to perform a random walk in the space of all Feynman diagrams. The DMC has been especially successful in solving polaron models, e.g. the Fr\"ohlich model for large polarons and the Holstein model for small polarons. These model systems can be solved with high accuracy but their applicability to real materials is questionable. Simplifications, like considering only a single, parabolic electron band and a single, dispersionless phonon branch in the Fr\"ohlich polaron, makes it difficult to connect the models to reality. Real materials have complex band structures, phonon dispersions and electron-phonon coupling. To account for this complexity, one usually has to resort to first principles methods, like density functional theory (DFT). Although DFT is capable of studying polarons in materials directly, it has its limitations and drawbacks. In this contribution, we explore and discuss a combination of DFT and DMC. DFT is used to calculate the electronic band structure, phonon dispersions and electron-phonon coupling in a material. These quantities are fed into a general polaron Hamiltonian which is then solved with DMC. This allows for a complete ab initio treatment of polarons without the drawbacks of model Hamiltonians or direct DFT calculations.