The lunar volcanic glasses and Mg-suite rocks represent the early enigmatic episodes of lunar magmatism. Due to the gravitational instability of the Fe-Ti enriched (+/- KREEP) layer, which is formed at the later stage of fractional crystallization, a post-magma-ocean cumulate overturn occurred contemporaneously or near-contemporaneously with the lunar magma ocean (LMO) solidification. The radioactive elements within the KREEP layer were transferred downward and provided continuous energy for the partial melting of the Moon's interior. The melt from the Moon's interior and those from decompression melting, in turn, provide source magma for the origin of lunar volcanic glasses and Mg-suite. However, experimental and theoretical studies on the formation process of lunar volcanic glasses and Mg-suite show that the origin of their parental magma is poorly constrained, which largely depends on the initial depth and composition of the LMO. This review examines the mineralogy, petrogenesis, and distribution of lunar volcanic glasses and Mg-suite. Combining with existing models, we constrain the degree, distribution, and timescale of lunar mantle overturn and explore their relationship with later stages of LMO differentiation. We propose an updated chemical composition of the lunar interior, which provides a useful reference for estimating the bulk composition and early differentiation of the Moon and the early Earth.