This article compares the “right to seek and enjoy asylum” enshrined in Art. 14 of the Universal Declaration of Human Rights with the current EU policy developments to “externalize” or “extraterritorialise” migration control and refugee protection. Examining the genesis of Art. 14 during the negotiations of the Universal Declaration, it is argued that while Art. 14 clearly falls short of granting a substantive right to be granted asylum, its formulation was intended to maintain a procedural right – the right to an asylum process. While the Universal Declaration is not a legally binding instrument, going back to the fundamental norms expressed herein nonetheless provides an important starting point for evaluating current policies, especially in light of recent critiques against overly expansive interpretation of human rights law. As such, the article concludes that the current EU policies to shift migration control and refugee protection away from Europe in important respects contravenes “the right to seek asylum” as it was conceived exactly 60 years ago.