Aluminosilicate glasses and melts are of great geological and technological importance. Significant efforts have been spent for enhancing the insight into their structures. Here magic-angle-spinning (MAS) NMR that exploits the spin-5/2(27)Al as probe nucleus constitutes one widely utilized option. We review the application of Al-27 NMR experimentation to aluminosilicate glasses, emphasizing practical aspects of performing MAS and triple-quantum MAS NMR experiments, as well as options for data analysis to extract Al-27 NMR parameters and quantifying AlOp populations. Despite that parts of the text apply generally to MAS NMR targeting half-integer spins as structural probes in both crystalline and amorphous materials, the focus remains on Al-27 NMR applications to aluminosilicate glasses, whose basic structural features are outlined together with a survey of the most central research problems in the field. The current update of our previous article from 2015 [Eden, Annu. Rep. NMR Spectrosc. 86 (2015) 237-331] also reviews the principles of heteronuclear NMR experimentation and its applications to study both the short (less than or similar to 0.3 nm) and medium (approximate to 0.3-1 nm) range structure of aluminosilicate glasses. Moreover, the present article also extends our previous account by reviewing some of the most recent work in the area up to the beginning of year 2020, where several sections are significantly modified and expanded. The presentation is intended for a broad audience, encompassing both experienced researchers in solid-state NMR and/or glass structures, as well as to beginners in either area.