The European Central Bank has published Working Paper No 3137, a chapter for the Research Handbook of Inflation (2025), taking stock of medium-sized New Keynesian Dynamic Stochastic General Equilibrium models used in central banks and academia to analyse inflation dynamics, monetary transmission and policy interventions. The authors emphasise that the canonical Smets and Wouters (2007) framework still explains euro area and US inflation and output dynamics despite lacking crisis-specific features, and note that the views are their own and not necessarily those of the ECB. In the canonical model, inflation is found to be driven mainly by price and wage mark-up shocks (standing in for broader cost-push forces such as energy and imported input prices), while demand shocks dominate GDP fluctuations, consistent with an estimated weak inflation–slack relationship and a stabilising countercyclical policy response. The 2021-2022 inflation surge is largely attributed to repeated and persistent cost-push shocks rather than overheating demand. The paper also traces the evolution of the ECB’s New Area-Wide Model (NAWM), including extensions adding financial frictions and effective lower bound features (NAWM II) and a more recent direct oil price channel, which is shown to improve conditional inflation forecasts during the energy-driven inflation surge when oil prices are used as conditioning information. On policy analysis, DSGE-based counterfactual exercises are presented as useful for assessing systematic policy choices: one set of “no-change” counterfactuals suggests inflation would have been higher by about 2.5 percentage points in 2023 and 3 percentage points in 2024 absent the tightening of the expected interest rate path since late 2021, while optimal-policy comparisons indicate ECB decisions in 2022-2023 were generally close to model-based prescriptions using real-time information, even though hindsight would imply a more aggressive response. Looking ahead, the chapter argues that recent inflation episodes exposed key modelling limitations, particularly linear dynamics and simplified supply-side structures, and calls for richer supply-side modelling and nonlinear features to better capture large price swings, supply chain disruptions and structural shifts such as climate change and digitalisation.