We consider non-Hermitian energy band theory in two-dimensional systems and study the non-Hermitian skin effect and eigenenergy braids on slices in the two-dimensional Brillouin zone. We show the consequences of reciprocity and geometric symmetry on both these effects. Through this, I will give also give a pedagogical introduction on eigenvalue braiding in non-Hermitian systems. If time permits, I will also describe another work by our group on the mesoscopic non-Hermitian skin effect in a waveguide quantum electrodynamics system.