The effectiveness of the international legal system and its capacity to be ‘universal’ is largely dependent on the attitude of domestic authorities towards international rules, which can be influenced by solutions provided in constitutions. Specific attention should be paid to the role and rank of sources of international law in domestic legal orders and their relationship with the constitution and other national sources. In the past, scholars identified three different approaches to this issue (Western constitutions, Socialist States and Third World countries). However, it is relevant to examine the current state of the art in contemporary constitutions, due to novelties concerning the attitude of States towards international sources. A survey of these texts reveals a spectrum of solutions, including: constitutions that ignore the topic; the express subordination of international law to the constitution and/or acts of Parliaments; and the predominance of general custom and/or international treaties over national legislation. This assessment clearly identifies some potential difficulties for international law to apply equally and indiscriminately across domestic legal systems even if a general survey indicates the increasing openness of contemporary constitutions towards international law. Consequently, a series of mechanisms have also been included in contemporary constitutions to solve conflicts between domestic and international rules. Nonetheless, in some instances, difficulties to reconcile international law with national constitutions can be recognised which contribute to undermining the ‘universal’ character of the international legal order.