Abstract Carbon allowances are a new class of financial instrument which aim to assist in limiting the extent and impact of global warming and climate change. The feedback mechanism in the “Carbon-Energy-Finance” system makes the information connectedness dynamics more complex since we add equity, bond and non-energy commodity assets into the system. Using modified error variance decomposition and network diagrams, we quantify and systematically analyze how the European carbon market connects with information from a wide range of other markets. Our results indicate: (i) the nature of information spillover changes over time, with system-wide return connectedness being higher and more variable than the volatility interdependence; (ii) both the oil and carbon markets closely connect with equity and non-energy commodity markets rather than bond markets; (iii) we identify three structural breaks in carbon volatility and their implication for carbon-finance linkages; (iv) financial risk-type macroeconomic factors make greater contributions to system-wide connectedness than commodity factors. These findings have economic implications for investors, portfolio managers and policymakers.