What is sovereign immunity and to what extent can ordinary citizens sue the federal or state governments?

Sovereign immunity, inherited from English common law, holds that the 'king can do no wrong' and prevents suits against the government without its consent. The Federal Tort Claims Act (1946) waived federal immunity for many tort claims arising from negligent or wrongful acts of government employees acting within the scope of their employment. However, critical exceptions remain: the discretionary function exception bars claims arising from government policy decisions, and the FTCA does not cover intentional torts like assault, battery, or defamation by most federal employees (though there is a law enforcement exception for some intentional torts). State sovereign immunity is separately governed by the 11th Amendment and each state's own laws, and varies considerably in scope.