This review considers the problem of the construction of formal solutions for resonant systems and several concepts related to resonance. In the first part we introduce the concepts of Hori's kernel and averaging (not to be confounded with the usual Krylov-Bogolyubov first-order definition of averaging). In the second part these concepts are used to discuss resonance in action-angle variables. The first averaging, the construction of resonant Hori's kernels, their topological and quantitative constraints, the second averaging and the occurrence of inner resonances are discussed. These topics are assembled without a preoccupation of reviewing the contributions of all authors that have dealt with them, but rather aiming at giving a global picture of the problem of the construction of complete theories.