Some properties of the old and new states of quarkonium as well as QCD based methods for studying those states are discussed. A general formula for observable effects of isospin violation in the production of heavy mesons in e⁺e^– annihilation is derived in Chapter 2. In addition the production and scattering amplitudes of heavy mesons with the presence of two closely spaced narrow resonances are studied. In Chapter 3 an alternative viable source of the X(3872) resonance with simple kinematics is suggested. Further, the transitions from resonance X(3872) to the χcJ states of charmonium with emission of one or two pions are considered. It is found that the relative rates for these transitions to final states with different J may shed light on the understanding of isotopic structure of the X(3872) and the prominence of the four-quark component in it’s internal dynamics. Chapter 4 is devoted to study of new J^PC = 1^–– resonances. It is argued that relatively compact charmonium states, J/ψ, ψ(2 S), χ_c, can very likely be bound inside light hadronic matter, in particular inside higher resonances made from light quarks and/or gluons. The charmonium state in such binding essentially retains its properties, so that the bound system decays into light mesons and a particular charmonium resonance. Such bound states of a new type, hadro-charmonium, may explain the properties of some of the recently observed resonant peaks, in particular of Y(4.26), Y(4.32–4.36), Y(4.66), and Z(4.43). Further possible implications of the suggested picture for the observed states and existence of other states of hadro-charmonium and hadro-bottomonium are discussed. In Chapter 5 it is argued that the existing analysis of the experimental data on the dipion transition ϒ(3 S) → ϒ(1S) ππ was incomplete and suggestions to remove the internal ambiguity are made.