The goal of my talk is to describe recent developments in the topic
of quantum corrections to the energy of classical solitons. The
basics in this matter were solidly founded in 1974 by Faddeev and
Korepin in Sankt-Petersburg and Dashen-Hasslacher and Neveu in
Princeton. Nevertheless, a new conceptual approach based in heat
kernel/zeta function regularization methods proved to be fruitful in
2002 both in the supersymmetric (Bordag, Goldhaber, van
Nieuwenhuizen, Vassilevich, Leipzig/Stony Brook) and bosonic
(Izquierdo, Fuertes, Guilarte, Leon, Oviedo/Salamanca) cases. This
year Vassilevich (Sao Paulo) extended the method to compute the
one-loop mass shift to non-commutative kinks, both purely bosonic
and supersymmetric. I will also comment on a subtle connection
between this subject and supersymmetric quantum mechanics.