  We discuss the origin of topological defects in phase transitions and analyze
their role as a "diagnostic tool" in the study of the non-equilibrium dynamics
of symmetry breaking. Homogeneous second order phase transitions are the focus
of our attention, but the same paradigm is applied to the cross-over and
inhomogeneous transitions. The discrepancy between the experimental results in
3He and 4He is discussed in the light of recent numerical studies. The possible
role of the Ginzburg regime in determining the vortex line density for the case
of a quench in 4He is raised and tentatively dismissed. The difference in the
anticipated origin of the dominant signal in the two (3He and 4He) cases is
pointed out and the resulting consequences for the subsequent decay of
vorticity are noted. The possibility of a significant discrepancy between the
effective field theory and (quantum) kinetic theory descriptions of the order
parameter is briefly touched upon, using atomic Bose-Einstein condensates as an
example.
