  Quantum Fisher information matrix (QFIM) is a core concept in theoretical
quantum metrology due to the significant importance of quantum Cram\'{e}r-Rao
bound in quantum parameter estimation. However, studies in recent years have
revealed wide connections between QFIM and other aspects of quantum mechanics,
including quantum thermodynamics, quantum phase transition, entanglement
witness, quantum speed limit and non-Markovianity. These connections indicate
that QFIM is more than a concept in quantum metrology, but rather a fundamental
quantity in quantum mechanics. In this paper, we summarize the properties and
existing calculation techniques of QFIM for various cases, and review the
development of QFIM in some aspects of quantum mechanics apart from quantum
metrology. On the other hand, as the main application of QFIM, the second part
of this paper reviews the quantum multiparameter Cram\'{e}r-Rao bound, its
attainability condition and the associated optimal measurements. Moreover,
recent developments in a few typical scenarios of quantum multiparameter
estimation and the quantum advantages are also thoroughly discussed in this
part.
