Classification results for non-mixed and mixed optimal covering codes: a survey

A survey is given that comprises the known classification results on non-mixed and mixed optimal covering codes. Several new, so far unpublished results of the author are declared and proved as well. The generality of the specified classification results are quite different. The proof of the more or less general new results are mostly combinatorial. In contrast with the latter, computer-aided proofs are given for numerous individual cases. The individual (old and new) classification results are merged and summarized in a set of tables