The recent state aid cases of Dôvera and Casa Regina Apostolorum demonstrate how competition and healthcare remains a contentious issue, highlighting tensions between both economic and social aspects, and EU and Member State competences. The approach taken by the EU courts typically emphasises total non-applicability of the state aid rules, although partial immunity via the Services of General Economic Interest (SGEI) mechanism is gaining greater recognition via cases such as Brussels Hospitals and successive Commission SGEI “packages”. With the State Aid Temporary Framework—introduced in response to the COVID-19 pandemic—support for various healthcare activities was facilitated via the Article 107(3) TFEU justifications. This chapter suggests that these three aspects—from non-applicability, via SGEI, to Article 107(3) TFEU—can offer further insight into where market forces can usefully be deployed in healthcare reform, and where these may have a detrimental effect. However, further understanding can be gained from examining constitutional aspects—not only Member State competence for healthcare under Article 168(7) TFEU, but also perceptions of “competence creep” at EU level regarding national healthcare, and implications for both levels of developing a European Health Union. This chapter advances discussions in this area by juxtaposing “competition” and “constitutionalism” perspectives, while drawing on insights from before and during the COVID-19 pandemic.