  We discuss the central and, mostly, spin-dependent potentials in heavy
quarkonia $\bar b b, \bar c c$, with two goals in mind. The first is
phenomenological: using the splitting between the 1S and 2S pairs, as well as
the 1P and 2P quartet masses, we obtain very accurate values of all matrix
elements of the spin-depepdent potentials. The second is theoretical: using
standard wave functions, we compute these matrix elements, from perturbative,
nonperturbative and ``string" contributions. The model for nonperturbative
effects is a ``dense instanton liquid model", in which the QCD vacuum is made
of (strongly color correlated) instanton-antiinstanton pairs or "molecules". We
calcuate their effect via standard Wilson lines, with or without extra powers
of gauge fields. We find that this model provides a reasonable description of
all central, spin-spin and spin-orbit forces at distances $r= 0-0.7 \, fm $,
relevant for $\bar b b $ and $\bar c c$ quarkonia.
