Similarly to the significant of the concept of permanent establishment (PE) for the purpose of income taxes rules, the relevance of the concept of fixed establishment (FE) for the VAT rules can hardly be overestimated. The term plays a central role, and is consistently relied upon by the legislator, for both determining the place of supply of services in VAT, and to establish the right to VAT refund, where tax is incurred in a country other than that where the business is established. Yet, despite its significance, the term is far from clear, and in recent years the debate over its definition and scope, primarily in the context of new, globalised, economic realities, and the development of the digital economy, has intensified. The aim of this chapter is to shed light over the meaning and significance of the concept of FE for VAT purposes. It will focus first on the meaning and significance of the concept from the perspective of European VAT legislation and the jurisprudence of the Court of Justice of the European Union (CJEU). It will then discuss current challenges to the current law posed by new economic realities, discrepant application of the FE criterion at national level, and its links to the PE concept. It is argued that the case law of the CJEU highlights the challenges posed by both globalisation, and digitalisation of the world economy, and that whilst it provides short-term relief to these challenges, dealing with them on a longer term basis will require re-assessment of established jurisprudence. It considers some of the key decisions on FE by national courts, concluding that whilst a unified concept of secondary establishment for the purposes of income tax and VAT is desirable, at present equating PE to FE would likely give rise to double taxation within VAT.