Recently, the hybrid cavity-magnon system has attracted considerable interest. Owing to the good tunability of magnons, it is promising to use the magnons as a core to implement a hybrid quantum platform for transferring information among different quantum systems. In this article, we first briefly review the cavity magnonic systems and clarify the coupling mechanism between magnons and microwave photons. Then, we introduce the latest research progress in the aspects of nonlinearity and pseudo-Hermiticity, including the bistability of cavity magnon polaritons, observation of the second-order exceptional point in a PT-symmetric hybrid cavity-magnon system, and the pseudo-Hermiticity with a third-order exceptional point.