We will present an introduction to the physics of exotic charmonium, describing
the most popular configurations proposed for these states: tetraquark and meson molecules. I will then show how these states can be produced in hadronic collisions and in heavy ion collisions, both in central and peripheral reactions. I
will present our latest results on the production cross sections, abundancies and rapidity distributions. The talk will be based on material published in arXiv:1704.08781; arXiv:1610.06604; arXiv:1604.07716 ; arXiv:1511.05209 and arXiv:1405.7583. Ongoing calculations will be presented.