Reserved powers

Reserved powers, residual powers, or residuary powers are the powers that are neither prohibited nor explicitly given by law to any organ of government. The doctrine of popular sovereignty (in republics) or parliamentary sovereignty (in constitutional monarchies) assumes that governments have the authority to legislate over any area that has not been explicitly forbidden by a prior agreement, such as a constitution, treaty, or human rights instrument.
Federations and confederacies.
In countries with multiple orders of government, such as federations and confederacies, the powers of the central government versus the regional governments is spelled out in the basic law or constitution. The issue then arises: which order of government should have the power to legislate over anything that is not explicit listed? Such powers, as well as general power of competence, are given because it is impractical to detail in legislation every act allowed to be carried out by the state.
Reserved powers are given to different orders of the government in different federations and confederations. Both types are distinguished by the fact that a "confederacy" is typically thought of as giving very few powers to the centre, with many reserved powers held by the member states. In history, confederacies have usually been loose alliances of tribal chiefdoms or small monarchies. Sovereignty was always held be the councils of chiefs, dukes etc.
Modern federations have arisen only since the adoption of popularly-elected governments, when the question becomes which of two elected assemblies should prevail if both claim jurisdiction over one piece of land. Contrary to popular American myth, the idea of two co-existing orders of government was neither invented by the Founding Fathers nor taken from the Iroquois League. After all, the colonial legislatures and the British parliament had co-existed for more than a century.
The American experience "did" influence all subsequent federations, however, because of the innovation of "listing" the particular powers of the central government and giving the all unlisted powers (the reserve powers) to the states. Initially after independence, in the Articles of Confederation, the central authority was quite weak. The second attempt, the Constitution of the United States, which was created in 1787 and ratified the following year, gave more listed powers to the centre but ultimately kept the residual powers in the states.
All subsequent federations have looked at previous examples when they drafted their list of powers and decided to which order of government to give the residual powers. For example, in the 19th century the Canadian constitutional drafters specifically reversed the American decision and gave reserve powers to the central government, whereas the Mexican and Australian drafters followed the American practice. As new federal constitutions have been written and amended, comparisons to those early models are frequently used as inspiration.
By region.
Australia.
In Australia, the reserved powers lie with the states, as inspired by the US model. Chapter 5 of the 1901 Constitution of Australia states: "Every power of the Parliament of a Colony which has become or becomes a State, shall, unless it is by this Constitution exclusively vested in the Parliament of the Commonwealth or withdrawn from the Parliament of the State, continue as at the establishment of the Commonwealth, or as at the admission or establishment of the State, as the case may be."
Canada.
In Canada, the reserved powers lie with the federal government per Section 92 of the Constitution Act 1867. This was explicitly done to be the opposite of the United States, as the Fathers of Confederation (notably Thomas D'Arcy McGee) thought that the concepts of states' rights and nullification had caused the American Civil War.
European Union.
The European Union has the principle of conferral.
Mexico.
In Mexico, the Constitution of 1824 gave the reserve powers and the power of the purse to the states.
United States.
In the United States, the Tenth Amendment of the Constitution states that any power not explicitly granted to the federal government lies solely in the states. However, since World War II, the Supreme Court has consistently ruled against cases challenging the powers of Congress, with exceptions during the Rehnquist Court. In effect, the Supreme Court has decided that Congress has the power to determine the scope of its own authority.