  Exotic quarkonia are candidates to new types of hadrons including four quarks
or gluonic degrees of freedom as constituents, the latter being a unique
feature of QCD. We review recent developments in nonrelativistic EFTs to
describe exotic quarkonia and in particular recent results on the spectrum of
heavy hybrids including spin-dependent contributions up to $1/m_Q^2$-terms in
the heavy-quark-mass expansion. We determine the nonperturbative contributions
to the matching coefficients of the EFT by fitting our results to lattice-QCD
determinations of the charmonium hybrid spectrum and extrapolate the results to
the bottomonium hybrid sector where lattice-QCD determinations are still
challenging. We also report on a recent new approach to quarkonium hadronic
transitions that does not use the twist expansion and uses the hybrid spectrum
as the intermediate octet states.
