The repeated occurrence of supply-chain disruptions since the COVID-19 pandemic reveals the need to complement traditional macroeconomic frameworks with approaches that better capture the complexity of modern economic productionstructures. This paper synthesises the findings of the ChaMP Research Network, highlighting how production network models and heterogeneity across firms, sectors and countries enrich our understanding of monetary policy transmission. Bycapturing input-output relationships between firms and economic sectors, these approaches show how the propagation and persistence of shocks depend on network structure, the position of sectors within the network – where central sectorsexert disproportionate influence – and differences and variations in price and wage flexibility. The inflationary effects of supply shocks tend to be amplified, while the effects of demand shocks, including monetary policy shocks, are dampened. Inaddition, large shocks can give rise to nonlinearities, such as a steepening of the Phillips curve. This aligns with the conclusions of the ECB’s most recent strategy assessment, which emphasise the need to analyse the risks surrounding the inflationoutlook. The findings also point to the emergence of trade-offs between inflation and output gap stabilisation, as production networks and heterogeneity weaken the alignment between price and output dynamics. As a result, stabilising inflation andoutput simultaneously calls for astute fiscal policy. Overall, incorporating production networks provides a more nuanced and policy-relevant framework for designing state-contingent and data-informed monetary policy.