Non-Hermitian, Topological, and Lorentz non-reciprocal photonic resonators have attracted intense attention due to their complexities which are strongly dependent on their spatial and temporal structures. Strongly dispersive materials such as plasmonic and gyromagnetic materials lead to additional difficulties in defining topological bands. In this talk, I will introduce recent progress in my group and discuss the bands and edge modes in these low-symmetry photonic systems. Arrays of plasmonic nanoparticles and gyromagnetic resonators will be used as examples to illustrate the topological and Lorentz non-reciprocal effects.