Compact quantum groups are natural carriers of symmetry in the framework of C*-algebras. Just like the theory of C*-algebras can be seen as a non-commutative version of topology, compact quantum groups can be viewed as a generalization of compact Hausdorff topological groups. In 1988, Woronowicz proved a Tannaka-Krein result for compact matrix quantum groups. After recalling and discussing the beauty of this theorem, we point out how it opens a door to combinatorial methods in the theory of quantum groups. In particular, we apply this Tannaka-Krein machinery to obtain Banica and Speicher's orthogonal easy quantum groups (their work from 2009). Then we apply it to unitary easy quantum groups (joint work in progress with Pierre Tarrago) and other versions of the "easy" type quantum groups (joint work in progress with Guillaume Cébron).