Quantum state discrimination (QSD) is a fundamental problem in quantum information science, whose central goal is to optimally distinguish nonorthogonal quantum states under limited resources. Due to the constraints imposed by the fundamental principles of quantum mechanics, nonorthogonal quantum states cannot be perfectly distinguished through a single measurement. However, under non-unitary evolution governed by a non-Hermitian Hamiltonian, initially nonorthogonal states can be evolved into orthogonal ones within a finite time, thereby achieving perfect discrimination and opening new avenues for quantum information processing. Specifically, parity-time (PT)-symmetric systems and P-pseudo-Hermitian (PPH) systems serve as two important platforms for the orthogonalization of nonorthogonal quantum states. By carefully designing Hamiltonians that satisfy the corresponding symmetry conditions, a system can evolve a pair of initially nonorthogonal states into orthogonal ones within a finite time, thereby enabling perfect discrimination through a single measurement. Moreover, under certain conditions, PPH systems can accomplish state discrimination with higher efficiency than PT-symmetric systems. In terms of experiments, the feasibility of non-Hermitian QSD has been verified on various physical platforms. Using linear-optical setups, researchers have realized PT-symmetric systems capable of discriminating two and three nonorthogonal quantum states. In optical systems, researchers have realized controllable non-unitary evolution through polarization control and loss engineering, experimentally observing periodic oscillations in quantum-state distinguishability within the unbroken PT-symmetric phase, as well as monotonic decay behavior in the broken phase. In trapped-ion systems, by precisely introducing dissipation, unambiguous discrimination of nonorthogonal quantum states has been achieved in both the unbroken and the broken PT-symmetric regions, with significant acceleration of quantum evolution observed under specific dissipation conditions. Furthermore, an experimental scheme embedding a two-dimensional non-Hermitian system into a three-dimensional Hermitian system has demonstrated the equivalence between PT-symmetric state discrimination and unambiguous state discrimination (USD) in Hermitian systems. To date, there have been no experimental studies on QSD in P-pseudo-Hermitian systems. In summary, research on non-Hermitian QSD not only deepens our understanding of non-unitary dynamics but also opens new avenues for efficient quantum information processing. Future work may further extend the application of non-Hermitian Hamiltonians in QSD, generalize these strategies to higher-dimensional and more generic non-Hermitian systems, and explore more diverse experimental implementations, thereby laying the foundation for the development of faster and more efficient quantum technologies.