Deconfined quantum critical points (DQCPs) describe continuous phase transitions beyond the Landau-Ginzburg-Wilson paradigm, occurring between two phases characterized by distinct symmetry breaking. The debate over whether genuine DQCPs exist in physical SU(2) spin systems or if the transitions are weakly first-order has been ongoing for many years. In this talk, I will first provide a brief introduction to the concepts of DQCPs, emphasizing their development through experimental and numerical findings and presenting theoretical perspectives. I will then present our quantum Monte Carlo simulations on two models: the checkerboard J-Q model, inspired by experimental observations in SrCu2(BO3)2, and a non-Hermitian easy-plane J-Q model, designed to investigate how non-Hermitian interactions influence transitions that exhibit DQCP behavior.