The　use　of　numerical　models　in　the　advanced　analysis　and　design　of　steel　structures,　particularly　under　extreme　loading　conditions,　is　becoming　increasingly　widespread.　A　crucial　component　of　such　models　is　an　accurate　description　of　the　material　response.　A　systematic　study　into　the　dynamic　constitutive　modelling　of　structural　steels　is　presented　herein.　The　key　features　of　the　dynamic　stress-strain　characteristics　of　structural　steels　at　various　strain　rates,　i.e.,　test　methods,　material　strength,　strain-rate　effect　index　and　strain-rate　effect　models,　are　examined　and　discussed.　Supplementary　SHPB　tests　on　both　normal-　and　high-strength　structural　steels　(Q235,　Q355,　Q460,　and　S960)　under　a　wide　range　of　strain　rates　up　to　5000　s(-1),　filling　gaps　in　existing　datasets,　are　then　carried　out.　A　database　of　dynamic　test　results,　containing　453　stress-strain　curves,　is　systematically　established　and　analyzed.　Finally,　a　continuous　dynamic　constitutive　model,　capturing　the　dependency　of　both　yield　strength　and　strain　rate,　is　proposed　to　predict　the　dynamic　stress-strain　response　for　structural　steels,　from　normal-　to　high-strength　material　(235-960　MPa),　and　from　static　to　high　strain　rate　loading　conditions　(up　to　5000　s(-1)).