The impressive spectrum of mesons owes its origin to the strong interactions of quarks known as Quantum ChromoDynamics (QCD). The mediators of the strong interaction, the gluons, couple to quarks in a peculiar way: at high energies the coupling constant is small and a perturbative approach works reasonably well; however at low energies, the coupling constant becomes large and a perturbative approach fails. Thus one needs to study the hadronic spectrum using models, where each has its own caveats, or use an a-priori method, where only the quark masses and the strong coupling constant are needed as input. Such a method is lattice field theory. This theory is most often applied to QCD and in that case it is called lattice QCD.
Understanding the spectrum of a nonperturbative non-abelian gauge theory turns out to be very difficult. The primary question is how the particles of the spectrum, in the case of QCD these are the mesons and the baryons, show themselves in the S-, or scattering matrix. Are they bound states or are they resonances. Where do their poles lie? And what are the couplings to the various channels? How do the poles evolve, if the quark masses are changed - can resonances become bound states? How high can resonance go? What determines the number of bound states and resonances in the spectrum?
While knowing more and more about hadrons is indeed very interesting, we also want to use what we already know in search for the yet-unknown. This is where transitions between heavy mesons and light resonances enter - for example, there is still room for large new-physics contributions in several types of flavor-changing processes, mostly those involving bottom quarks - one of the major puzzles in flavor physics concerns the CKM matrix element Vub which appears in the b → ulν transitions. In the Standard Model of Particle Physics, these occur at the tree level through a W-boson exchange, and currently there is a discrepancy between the extractions of Vub from inclusive (when a B-meson decays to all possible light hadrons and lepton-anti-neutrino pair) and exclusive (currently only the decay of a B-meson to a pion and lepton-anti-neutrino pair) analyses.