Quantum estimation theory is essential for determining the precision of parameter estimation in quantum systems. Many quantities of interest in quantum information, such as entanglement and purity, are nonlinear functions of the density matrix and cannot correspond to proper quantum observables. Therefore, indirect measurements are required, which involve parameter estimation. Local quantum estimation theory focuses on optimizing the Fisher information to minimize the variance of the estimator, providing better performance than global estimation. The quantum Fisher information (QFI) sets the ultimate bound on the precision of parameter estimation, and it is related to the geometry of quantum statistical models. The QFI can be calculated using the symmetric logarithmic derivative (SLD) and is crucial for evaluating the ultimate precision of quantum measurements. The paper reviews local quantum estimation theory, presents formulas for the SLD and QFI for relevant quantum states, and discusses the connection between the optimization procedure and the geometry of quantum statistical models. It also addresses the quantification of estimability in terms of the quantum signal-to-noise ratio and the number of measurements needed to achieve a given relative error. The analysis provides tools for characterizing signals and devices in quantum technology. The paper concludes with a discussion on the geometric structure of quantum estimation and its implications for quantum information protocols.Quantum estimation theory is essential for determining the precision of parameter estimation in quantum systems. Many quantities of interest in quantum information, such as entanglement and purity, are nonlinear functions of the density matrix and cannot correspond to proper quantum observables. Therefore, indirect measurements are required, which involve parameter estimation. Local quantum estimation theory focuses on optimizing the Fisher information to minimize the variance of the estimator, providing better performance than global estimation. The quantum Fisher information (QFI) sets the ultimate bound on the precision of parameter estimation, and it is related to the geometry of quantum statistical models. The QFI can be calculated using the symmetric logarithmic derivative (SLD) and is crucial for evaluating the ultimate precision of quantum measurements. The paper reviews local quantum estimation theory, presents formulas for the SLD and QFI for relevant quantum states, and discusses the connection between the optimization procedure and the geometry of quantum statistical models. It also addresses the quantification of estimability in terms of the quantum signal-to-noise ratio and the number of measurements needed to achieve a given relative error. The analysis provides tools for characterizing signals and devices in quantum technology. The paper concludes with a discussion on the geometric structure of quantum estimation and its implications for quantum information protocols.