Classical coding theory arose as a mathematical model used to ensure error free communication. In this setting, codes were defined as vectors spaces where the alphabet was a finite field.  We shall describe the passage from classical coding theory to present day coding theory, viewing it as a subbranch of algebra, where codes are modules over finite Frobenius rings.  We shall focus on the generalization of the Singleton bound and on the MacWilliams relations which illustrate the passage.  We shall also present various applications of the most general form of coding theory in other branches of mathematics.