The genetic code (GC) plays a central role in all living organisms. From a mathematical point of view, the GC is a map from a set of 64 elements (which are codons) onto a set of 21 elements (which are 20 amino acids and 1 stop signal). The GC is the result of evolution, experimentally deciphered as early as the mid-1960s, but its satisfactory theoretical understanding does not yet exist. There are many papers on the GC modeling, its origin and evolution, but also many unsolved issues. In this contribution we provide a brief overview of genetic code modeling, highlighting the p-adic approach, which can describe many properties of the GC. Our primary mathematical tool is a p-adic distance, which simply and adequately describes similarities within the GC. We also point how one could apply this mathematical method to other sequences with a bioinformatic content.