The interplay between topology, Floquet engineering, and twistronics is currently revolutionizing our understanding of electronic systems. Can these ideas allow us to unveil new phases and phenomena in magnetic systems? I will answer these questions, in part, by addressing a major limitation in our current understanding within the field, i.e., how the topological properties of magnons, the quanta of magnetic excitations, remain poorly explored experimentally because of their inherently dissipative nature. I will discuss how the recent introduction of non-Hermitian topological classifications has opened up opportunities for engineering topological phases in dissipative systems, and I will present our first proposal of a non-Hermitian topological magnonic system, i.e., a realization of a SSH non-Hermitian model via a one-dimensional spin-torque oscillator array.