Although the relationship between EU law and Member State law is generally frictionless, it is regularly under strain in those hard cases where EU law clashes with the Member States’ constitutions. In that instance, there is a conflict between two equally legitimate claims: the supremacy claim of the constitution and the primacy claim of EU law. That conflict has been especially salient with regard to fundamental rights. Constitutional courts and the CJEU safeguard them to varying degrees depending on the right at issue, but also on the logic and constraints of the respective legal orders that they should protect. Constitutional courts are thus reluctant to give a blank cheque to the CJEU and give up their fundamental rights review. Likewise, the CJEU is reluctant to defer to national standards of protection. This chapter describes that tension, how it has gradually been largely overcome and why the issue of the level of protection of fundamental rights remains a bone of contention. It also takes a normative approach based on constitutional pluralism and argues in favour of an enhanced accommodation of higher national standards in EU law.