Article 36.1.b) of the Vienna Convention on Consular Relations of 1963 defines the “consular rights” we will reflect upon in this essay. They have not merited special attention for decades, although their adoption was achieved in extremis during the 1963 international conference. They are a clear example of progressive development of the Law of Consular Relations, both then and nowadays as they have been developed through recent international jurisprudence (at different courts: Inter-American Court of Human Rights, International Court of Justice and European Court of Human Rights). These tribunals have established relevant connections between these consular rights and the guarantees in case of detention and the right to a fair trial. Along with the jurisprudence, the European Union has ruled on those rights in several instruments, and Spain more or less accordingly, strengthening the connection with the idea of fundamental rights. The essay analyses national rules for non-criminal detention cases, too, before concluding on the present nature and effect of the consular rights.