  We give a survey of some recent results on the fusion semirings of compact
quantum groups (computations of and applications to discrete quantum groups) by
using the following simplifying terminology: we say that a compact quantum
group G is an R^+-deformation of a compact quantum group H if their fusion
semirings are isomorphic. The paper contains also some easy related results
(with proofs), two conjectures and many remarks and comments, some of them
concerning classification by invariants related to R^+.
