In this article, we aim to study systemic risk spillovers for European energy companies and to determine the spillover network of the energy sector with other economic sectors. To examine the spillovers within the energy sector, we employ three systemic risk measures. We then embed the results of these models into a Diebold–Yilmaz framework. Moreover, we consider an entropy procedure to extract a Bayesian formulation of its systemic risk spillover. This allows us to determine which company in our sample contributes the most to systemic risk, which company is the most vulnerable to systemic risk, and the place of the energy sector within risk networks. Our results reveal the fact that all companies manifest enhanced spillovers during 2008, early 2009, and 2020. These episodes are associated with the dynamics of the global financial crisis and the pandemic crisis. We notice that specific companies are risk drivers in the sector in both times of market turbulence and calm. Lastly, we observe that several economic sectors such as banks, capital goods, consumer services, and diversified financials generate relevant spillovers towards the energy sector.