The book examines one of the most debated issues in current international law: to what extent the international legal system has constitutional features comparable to what we find in national law. This question has become increasingly relevant in a time of globalization, where new international institutions and courts are established to address international issues. Constitutionalization beyond the nation state has for many years been discussed in relation to the European Union. This book asks whether we now see constitutionalization taking place also at the global level. The book investigates what should be characterized as constitutional features of the current international order, in what way the challenges differ from those at the national level and what could be a proper interaction between different international arrangements as well as between the international and national constitutional level. Finally, it sketches the outlines of what a constitutionalized world order could and should imply. The book is a critical appraisal of constitutionalist ideas and of their critique. It argues that the reconstruction of the current evolution of international law as a process of constitutionalization -against a background of, and partly in competition with, the verticalization of substantive law and the deformalization and fragmentation of international law- has some explanatory power, permits new insights and allows for new arguments. The book thus identifies constitutional trends and challenges in establishing international organisational structures, and designs procedures for standard-setting, implementation and judicial functions.This paperback edition features the authors' discussion of this book on the EJIL Talks blog.