Non-Hermitian systems have recently garnered widespread attention. Some non-Hermitian systems that satisfy parity-time reversal symmetry may possess real eigenenergy spectra and can be used to describe open systems with loss and gain. Their eigenenergy spectra exhibit strong nonlinear responses to external perturbations near exceptional points, which is a characteristic that can be harnessed to design implementations for quantum metrology and quantum sensing. Quantum-parameter estimation theory, which uses the quantum Fisher information, provides the quantum Cramér-Rao lower bound for parameter estimation, which sets a limit on the sensitivity of quantum measurements and sensing. Additionally, quantum-parameter estimation theory guides the search for optimal measurement schemes, and some optimal measurement results can be achieved within the quantum Cramér-Rao bound. In schemes that leverage the advantages of quantum resources, such as quantum entanglement, the estimation precision can surpass the standard quantum limit and reach the Heisenberg scaling. Additionally, some non-Hermitian systems may demonstrate enhanced sensitivity to external perturbations without involving exceptional points owing to their non-Hermitian nature, thus allowing non-Hermitian sensing schemes to be realized. This review introduces the research and progress in quantum metrology and sensing based on non-Hermitian systems.