Solid-state nuclear magnetic resonance (NMR) spectroscopy offers an array of options for exploring structural order of amorphous materials both over short (0.3 nm) and medium (1 nm) ranges. We review the advances reported in the literature for characterizing the structures of oxide-based glasses over roughly the past 15 years. Besides describing the current understanding of basic short-range structural aspects of binary and ternary glass systems that typically involve a single glass modifier and one (silicates and phosphates) or two (e.g., aluminosilicates, aluminophosphates and silicophosphates) network formers, we focus on illustrating the progress made for revealing intermediate-range structural order, such as extracting information about connectivities among the basic building blocks in the glass networks and how more extended structural motifs may be identified. By assuming only relatively basic background in solid-state NMR and/or the structure of glasses, we hope this review will appeal to newcomers of either area.