Incident management is a classical topic in cyber security. Recently, the European Union (EU) has started to consider also the relation between cyber security incidents and cyber security crises. These considerations and preparations, including those specified in the EU’s new cyber security laws, constitute the paper’s topic. According to an analysis of the laws and associated policy documents, (i) cyber security crises are equated in the EU to large-scale cyber security incidents that either exceed a handling capacity of a single member state or affect at least two member states. For this and other purposes, (ii) the new laws substantially increase mandatory reporting about cyber security incidents, including but not limited to the large-scale incidents. Despite the laws and new governance bodies established by them, however, (iii) the working of actual cyber security crisis management remains unclear particularly at the EU-level. With these policy research results, the paper advances the domain of cyber security incident management research by elaborating how European law perceives cyber security crises and their relation to cyber security incidents, paving the way for many relevant further research topics with practical relevance, whether theoretical, conceptual, or empirical.