Topological Defects in QCD at large Baryon Density and/or large $N_c$

The main leitmotiv of the present talk is analysis of different topological objects such as strings and domain walls in QCD. As it is well known, the standard model in general (and QCD in particular) does not support any kind of such objects due to some simple topological arguments. However, the situation cardinally changes when one considers QCD in large $N_c$ limit or in the limit of large baryon density when the unique light $\eta'$ field emerges. I discuss $\eta'$- domain walls and $\eta'$ global strings which occur in both systems: in high density QCD and in QCD at large $N_c$. I also discuss the effects of quantum anomalies in the presence of topological objects in high-density QCD. The anomaly induced interactions lead to a number of interesting phenomena (such as the induced currents along the strings) which may have phenomenological consequences observable in neutron stars.