  Quantum fluctuations generate in three-dimensional gauge theories not only
radiative corrections to the Chern-Simons coupling but also non-analytic terms
in the effective action. We review the role of those terms in gauge theories
with massless fermions and Chern-Simons theories. The explicit form of
non-analytic terms turns out to be dependent on the regularization scheme and
in consequence the very existence of phenomena like parity and framing
anomalies becomes regularization dependent. In particular we find
regularization regimes where both anomalies are absent. Due to the presence of
non-analytic terms the effective action becomes not only discontinuous but also
singular for some background gauge fields which include sphalerons. The
appearence of this type of singularities is linked to the existence of nodal
configurations in physical states and tunneling suppression at some classical
field configurations. In the topological field theory the number of physical
states may also become regularization dependent. Another consequence of the
peculiar behaviour of three-dimensional theories under parity odd
regularizations is the existence of a simple mechanism of generation of a mass
gap in pure Yang-Mills theory by a suitable choice of regularization scheme.
The generic value of this mass does agree with the values obtained in
Hamiltonian and numerical analysis. Finally, the existence of different
regularization regimes unveils the difficulties of establishing a Zamolodchikov
c-theorem for three-dimensional field theories in terms of the induced
gravitational Chern-Simons couplings.
