The EU customs system is currently a complex arrangement of customs institutions operating within the public and market space of the European Union, institutions which are strongly interlinked and perform multi-faceted tasks resulting from present challenges of the customs policy. The aim of the article is to analyze the definition of the customs system as well as to characterize the legal and organizational dimensions of the Union customs system against the background of challenges related to globalization, with a particular focus on customs administrations of Member States. The methodology employed in the paper consists in a descriptive analysis, preceded by a review of the subject literature and the EU secondary legislation as well as a comparative analysis. The research findings allowed a conclusion to be drawn that the customs system of the European Union efficiently and effectively adapts to new challenges and ever-increasing demands resulting from the changing conditions of the international trade, both in the legal aspect, i.e. regulations on trade in goods, as well as in the organizational dimension, i.e. activities of EU institutions shaping the customs system and customs administrations of Member States.