The muon anomalous magnetic moment is one of the most precisely measured quantities in particle physics, with a recent Brookhaven experiment achieving a precision of 0.54 parts per million (ppm), a 14-fold improvement over previous CERN experiments. Despite this high precision, a 3-standard-deviation discrepancy between the experimental value and the Standard Model (SM) prediction persists, making it the largest deviation from the SM seen in a clean electroweak observable. This discrepancy has sparked numerous speculations about the origin of the "missing piece" and has driven new theoretical efforts to improve the prediction of the muon anomaly \(a_{\mu} = (g_{\mu} - 2)/2\). The dominant uncertainty in the prediction, caused by strong interaction effects, has been significantly reduced due to new hadronic cross-section measurements in electron-positron annihilation at low energies. The recent electron \(g-2\) measurement at Harvard also contributes to this progress by allowing for a more precise determination of the fine structure constant \(\alpha\) and cross-checking the theoretical understanding. This report reviews the theory of the anomalous magnetic moments of the electron and muon, including the principle of the muon \(g-2\) experiment. It discusses the status of the theoretical prediction, focusing on the role of hadronic vacuum polarization effects and hadronic light-by-light scattering corrections, including a new evaluation of the dominant pion-exchange contribution. The report finds a 3.2-standard-deviation discrepancy between the experiment and the SM prediction. It also explores how extensions of the electroweak Standard Model would change the theoretical prediction of the muon anomaly \(a_{\mu}\). Perspectives for future developments in both experiment and theory are briefly discussed, highlighting the muon \(g-2\) as a hot topic for further investigations.The muon anomalous magnetic moment is one of the most precisely measured quantities in particle physics, with a recent Brookhaven experiment achieving a precision of 0.54 parts per million (ppm), a 14-fold improvement over previous CERN experiments. Despite this high precision, a 3-standard-deviation discrepancy between the experimental value and the Standard Model (SM) prediction persists, making it the largest deviation from the SM seen in a clean electroweak observable. This discrepancy has sparked numerous speculations about the origin of the "missing piece" and has driven new theoretical efforts to improve the prediction of the muon anomaly \(a_{\mu} = (g_{\mu} - 2)/2\). The dominant uncertainty in the prediction, caused by strong interaction effects, has been significantly reduced due to new hadronic cross-section measurements in electron-positron annihilation at low energies. The recent electron \(g-2\) measurement at Harvard also contributes to this progress by allowing for a more precise determination of the fine structure constant \(\alpha\) and cross-checking the theoretical understanding. This report reviews the theory of the anomalous magnetic moments of the electron and muon, including the principle of the muon \(g-2\) experiment. It discusses the status of the theoretical prediction, focusing on the role of hadronic vacuum polarization effects and hadronic light-by-light scattering corrections, including a new evaluation of the dominant pion-exchange contribution. The report finds a 3.2-standard-deviation discrepancy between the experiment and the SM prediction. It also explores how extensions of the electroweak Standard Model would change the theoretical prediction of the muon anomaly \(a_{\mu}\). Perspectives for future developments in both experiment and theory are briefly discussed, highlighting the muon \(g-2\) as a hot topic for further investigations.