  In this thesis we discuss a rational and data-based description of the
single- and double-virutal transition form factors of the lightest pseudoscalar
mesons. We obtain an accurate description of these in the spacelike and
low-energy timelike regions. The phenomenological applications are wide. Among
them, we discuss, the eta-eta' mixing, the rare pseudoscalar decays into a
lepton pair and the pseudoscalar-pole contribution to the hadronic
light-by-light part of the anomalous magnetic moment of the muon. In all these
cases we discuss and illustrate the relevance of employing a data-based
approach in order not to incur in potential systematic errors.
