Complex –passive or active- nematic fluids are characterised by internal orientational order, which upon tuning or frustration, can exhibit topological defects. The type of defects and their role naturally depend on dimensionality of the system, but importantly also on the geometry, confinement, flow, driving or even activity. Here, we present structures of topological defects in passive and active nematic complex fluids – forming umbilic defects, singular loops, point defects and disclinations. Specifically, we show in passive nematics how confinement in the form of complex geometry and fractal surfaces can lead to formation of various defect-based nematic profiles, including exhibiting high-elastic multipoles. In active nematics, we show defect profiles in three-dimensional active nematic droplet, also highlighting the role of different surface coupling regimes.