High-level descriptions of quantum algorithms do not take the restrictions of physical hardware into account. Therefore actually executing an algorithm in the form of a quantum circuit on a quantum computer requires compiling it for the desired target architecture first. The compilation of quantum circuits depends on efficient methods to be feasible for all but the trivial instances. To this end, different compiling methods have been introduced in the past, but room for improvement still exists. Moreover, just an efficient compilation process itself is not sufficient—the resulting circuits must be correct as well. In this summary paper, we review how existing compilation approaches can be optimized by utilizing heuristic search algorithms or exact reasoning engines. Furthermore, we review how the correctness of the obtained results can be verified afterwards by clever data structures such as decision diagrams. This illustrates core steps of a compilation flow which can generate minimal or close-to-minimal results for many instances and, additionally, guarantees correctness throughout the process.