Densification of oxide glasses at the glass transition offers a novel route to develop bulk glasses with tailored properties for emerging applications. Such densification can be achieved in the technologically relevant pressure regime of up to ~1 GPa. However, the present understanding of the composition-structure-property relationships governing these glasses is limited, with key questions, e.g., related to densification mechanism, remaining largely unanswered. Recent advances in structural characterization tools and high-pressure apparatuses have prompted new research efforts. Here, we review this recent progress and the insights gained in the understanding of the influence of isostatic compression at elevated temperature (so-called hot compression) on the compositionstructure-property relationships of oxide glasses. We focus on compression at temperatures at or around the glass transition temperature (Tg), with relevant comparisons made to glasses prepared by pressure quenching and cold compression. We show that permanent densification at 1 GPa sets in at temperatures above 0.7Tg and the degree of densification increases with increasing compression temperature and time, until attaining an approximately constant value for temperatures above Tg. For glasses compressed at the same temperature/pressure conditions, we demonstrate direct relations between the degree of volume densification and the pressure-induced change in micromechanical properties such as hardness, elastic moduli, and extent of the indentation size effect across a variety of glass families. Finally, we review the results on relaxation behavior of hot-compressed glasses. In summary, all the pressure-induced changes in the structure and properties exhibit strong composition dependence. The experimental results highlight new opportunities for future investigation and identify research challenges that need to be overcome to advance the field.