We present an overview of a novel entropy-based framework for analyzing structural ordering, relaxation propensity, and glass-forming ability (GFA) of metallic glasses (MGs) and their melts. The key idea of this approach consists in determining the excess entropy ΔS of the glass relative to the crystal. The quantity ΔS is highly sensitive to structural changes in MGs upon heat treatment within the non-crystalline state. ΔS is found to be inversely correlated with the mixing entropy ΔS_mix. A dimensional structural order parameter is introduced, which is effective for describing the structural evolution of MGs and correlates with the GFA of the melt. The relationship between ΔS and fragility is discussed; the excess entropy per atom and the entropy of structural "defects" in MGs are analyzed. The applicability of the approach to non-metallic glasses is briefly considered.