During the last three years strong experimental evidence from B and charm factories has been accumulating for the existence of exotic hadronic quarkonia, narrow resonances which cannot be made from a quark and an antiquark. Their masses and decay modes show that they contain a heavy quark-antiquark pair, but their quantum numbers are such that they must also contain a light quark-antiquark pair. The main theoretical challenge has been to determine the nature of these resonances. The main possibilities are that they are either “genuine tetraquarks”, i.e. two quarks and two antiquarks within one confinement volume, or “hadronic molecules” of two heavy-light mesons. In the last few months there is more and more evidence in favor of the latter. In addition, there exist narrow resonances such as X (3872) which are not exotic but are closely related to the exotic states. Most likely such states are a mixture of hadronic molecules and excited quarkonia. I discuss the experimental data and its interpretation and provide fairly precise predictions for masses and quantum numbers of the additional exotic states which are naturally expected in the molecular picture but have yet to be observed. In addition, I provide arguments in favor of the existence of an even more exotic state – a hypothetical deuteron-like bound state of two heavy baryons. I also consider “baryon-like” states QQ′qq′ , which if found will be direct evidence not just for near-threshold binding of two heavy mesons, but for genuine tetraquarks with novel color networks. I also stress the importance of experimental search for doubly-heavy baryons which are intimately connected with doubly heavy exotics.