The Tenth Amendment to the Constitution says, “The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.” These powers are often referred to as reserved powers. They include all authority and functions of state and local governments. Examples include election laws and administration, policing, education, health, environmental regulation, and business regulation.
The Tenth Amendment does not mean that the states can do anything they wish. On the one hand, the Supremacy Clause in Article 6 of the Constitution asserts the Constitution and constitutionally permitted federal laws and treaties are the supreme law of the land. Note also that the Supremacy Clause was the foundation of the Marbury v. Madison (1803) ruling, which found federal judges have the authority to declare a law unconstitutional.
On the other hand, the framers did explicitly limit the states in a few areas. While each state can maintain its own militia, Article 1, Section 10 denies states the right to maintain their own standing professional armies or navies. The same article also says the states may not negotiate foreign treaties, create their own coin money, make laws allowing contracts to be broken, grant titles of nobility, make ex post facto laws, or make bills of attainder by which legislatures convict people of crimes. (The last three powers are also denied to Congress by Article 1, Section 9.)
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 State banks issued notes tantamount to paper money until the National Banking Acts of 1863 and 1864 taxed them out of existence. https://www.senate.gov/artandhistory/history/common/civil_war/NationalBankActs.htm
Image: Reserved table, CC0, MaxPixel.net.