  The resummation of logarithms in Quantum Field Theories is a long tale plenty
of successes, yet the resummation of logarithms in non-relativistic theories
has remained elusive. This was the most frustrating, since the first quantum
field theory log ever computed was the Lamb shift one. We briefly review recent
progress on the resummation of logarithms of $\alpha$, which appear in the
physics of non-relativistic states, using effective field theories. We put
special emphasis on the basic formalism.
