The article looks, first, at what shapes the structure of intergovernmental relations (IGR), and, second, at the structures themselves. With respect to the factors that shape IGR, the paper identifies six: demographic and geographical; social and cultural; historical; constitutional and institutional; political; and circumstantial. With respect to the structures themselves, the paper notes that the degree of institutionalisation, the extent to which IGR is decisionmaking in character, and the degree of transparency all help to define the IGR system. The paper then goes on to categorise IGR into four dimensions: intra-jurisdictional IGR, in which the institutions at the centre are 'federalised'; inter-jurisdictional IGR, in which the defining feature is the character of the relations between and among the central and regional governments; IGR and the judiciary, in which the appeal to the courts becomes the extension of IGR into a different arena; and international and other forms of IGR, involving quasi-governmental international bodies, multitiered political structures transcending the parameters of states, and forms of indigenous self-government. The article closes by arguing that democratising IGR is one of the central challenges confronting governance at the beginning of the new century.