After the accession of several Central and Eastern European countries to the European Union in 2004, new challenges arose for their highest judicial institutions to define and shape the relationship between the national and European legal order. This paper assesses the first decade of the effort of the Slovak Constitutional Court (SCC) in interpreting the relationship between domestic and EU law via applying the concept of constitutional pluralism which presumes a specific relationship between the legal orders characterized by their heterarchical structure, mutual interaction and cooperation rather than of a hierarchical, monistic structure, governed by clash over dominance. Answering the research question how the SCC has positioned itself vis-à-vis the constitutional monism v. pluralism dilemma can offer an insight on the general relationship between domestic and EU law in Slovakia. By analysing statutory law, selected judgments and reviewing secondary literature, the paper argues that the SCC seems to have chosen the monistic, hierarchical approach to the relationship, having rejected constitutional pluralism. At the same time, this position is not articulated clearly enough due to the veil of secrecy that to some extent still prevails over the SCC’s doctrinal attitudes to EU law. The findings of the paper, which combines conceptual analysis of constitutional pluralism with review of relevant legal provisions and case law, demonstrate the need for a more active and straightforward approach of the SCC when dealing with the challenges of EU law.