Abstract: For several decades, the quark model suggested 60 years ago as a classification scheme for multiquark states had been a powerful and successful tool to understand and predict properties of various hadronic states in QCD. However, since 2003, when the Belle Collaboration discovered the X(3872), an enigmatic state in the spectrum of charmonium with the properties at odds with the predictions of the quark model, a new era in the spectroscopy of hadrons containing heavy quarks began. Since then, many new states in the spectrum of charmonium and bottomonium have been discovered that do not fit into the quark model scheme and qualify as exotic states. Most of them reside near strong open-flavour thresholds that leave imprint on their nature and properties. I will discuss theoretical approaches to extracting the information contained in the experimental data on exotic hadrons with heavy quarks and how this information can be used to make predictions for not yet observed hadrons and their properties.