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 which do not fit into the quark model scheme and as such qualify as exotic states. Most of such states are narrow and reside near strong open-flavour thresholds, which therefore leave imprint on their properties. I will discuss the theoretical approach to exotic states with heavy quarks based on the Effective Field Theory (EFT) and address some relevant specific issues such as the role of coupled channels, multibody dynamics, low-energy expansion of the amplitude, interplay of the quark and hadronic degrees of freedom, and so on. Theoretical analysis of the experimental and lattice data for the double-charm state Tcc+ found recently by the LHCb collaboration at CERN will be considered as a paradigmatic example.