  A closed subgroup $G\subset_uU_N^+$ is called easy when its associated
Tannakian category $C_{kl}=Hom(u^{\otimes k},u^{\otimes l})$ appears from a
category of partitions, $C=span(D)$ with $D=(D_{kl})\subset P$, via the
standard implementation of partitions as linear maps. The examples abound, and
the main known subgroups $G\subset U_N^+$ are either easy, or not far from
being easy. We discuss here the basic theory, examples and known classification
results for the easy quantum groups $G\subset U_N^+$, as well as various
generalizations of the formalism, known as super-easiness theories, and the
unification problem for them.
