In this habilitation defense, I give a subjective overview of some recent progress in solving two-dimensional conformal field theories. I discuss what solving means and which techniques can be used. I insist that there is much to discover about Virasoro-based CFTs, i.e. CFTs that have no symmetries beyond conformal symmetry. I claim that we should start with CFTs that exist for generic central charges, because they are simpler than CFTs at rational central charges, and can nevertheless include them as special cases or limits. Finally, I argue that in addition to writing research articles, we should use various other media, in particular Wikipedia. \\ \\ Members of the jury: Denis Bernard, Matthias Gaberdiel, Jesper Jacobsen, Vyacheslav Rychkov, Véronique Terras, Gérard Watts, Jean-Bernard Zuber.