We give a comprehensive review of the algebraic approach to the genetic cod
e originally proposed by two of the present authors, which aims at explaini
ng the degeneracies encountered in the genetic code as the result of a sequ
ence of symmetry breakings that have occurred during its evolution. We pres
ent the relevant background material from molecular biology and from mathem
atics, including the representation theory of (semi) simple Lie groups/alge
bras, together with considerations of general nature.