Solar eruptions are outbursts of magnetized plasma in the atmosphere of the Sun, encompassing phenomena like solar flares, ejective prominences and coronal mass ejections. Their induced disruptive space weather conditions can profoundly impact various aspects of human activities, ranging from ground-based infrastructure to space-borne technology. Nonetheless, the question of how solar eruptions originate has remained a subject of ongoing debates over decades. In this review, we present recent advancements in our quest to establish a fundamental mechanism with both simplicity and efficacy for the initiation of solar eruptions, based on numerical magnetohydrodynamics simulations. Our proposed mechanism centers around the gradual development of an internal current sheet within a continuously sheared magnetic arcade as driven by photospheric motions and fast reconnection at this current sheet initiating alone the eruption without the need of other factors. With a range of simulation experiments, we have shown that the mechanism can operate with both bipolar and multipolar fields, and in both emerging and decaying phases of solar active regions, provided that there exists a photospheric driving motion that can efficiently increase the degree of the coronal field non-potentiality. Based on this mechanism, models for homologous eruptions and failed eruption are also proposed, and additionally, explanations are provided for the associated phenomena during eruption, such as formation and rotation of the erupting magnetic flux rope, contraction of the peripheral coronal loop, as well as rapid enhancement of the photospheric horizontal field along the flare polarity inversion line. Data-inspired and data-driven simulations have been further performed for realistic eruption events which validate the fundamental mechanism. Finally, we discuss future developments of the mechanism and its possible application in prediction of solar eruptions.
