Inthistalkwewillsurveymethodsfortheapproximationoflarge-scaledynamicalsystems.Therearetwobasicfamilies,namelytheSVD-basedandKrylov-basedapproximationmethods.Theformerfamilyisbasedonthesingularvaluedecompositionandthesecondonmomentmatching.Whiletheformerhasmanydesirablepropertiesinclud