  We trace the origin of theta-terms in non-linear sigma-models as a
nonperturbative anomaly of current algebras. The non-linear sigma-models emerge
as a low energy limit of fermionic sigma-models. The latter describe Dirac
fermions coupled to chiral bosonic fields. We discuss the geometric phases in
three hierarchies of fermionic sigma-models in spacetime dimension (d+1) with
chiral bosonic fields taking values on d-, d+1-, and d+2-dimensional spheres.
The geometric phases in the first two hierarchies are theta-terms. We emphasize
a relation between theta-terms and quantum numbers of solitons.
