Under the Taking Clause of the Fifth Amendment, state and federal governments can garner private property for public use with "just compensation." If a government action is not considered a "taking" under the Fifth Amendment, then the government would not be required to provide compensation.
In Penn Central Transportation Company v. New York, the Supreme Court ruled that the Landmarks Preservation Law which prevented Penn Central to build a multistory building above the complex was not considered to be a "taking" under the Fifth Amendment. Thus, the New York state government was not compelled to provide compensation.
In Lucas v. South Carolina Coast Council, Lucas purchased two residential lots with the intention to construct family homes. However, the state had passed a law which prevented the building of habitable structures in order to prevent erosion and preserve the barrier islands. The Supreme Court ruled in favor for Lucas, stating that the law constituted a "taking" and thus required "just compensation." The justification is that due to the law, Lucas's land was valueless which would have originally would have had value if the law was not enacted.
One of the major requirements behind the Takings Clause is if the purpose of the property being taken by the federal government has a "public use".
A major and recent case tackling the limits of the requirement is the 2005 Kelo v. City of New London. New London, Connecticut sought to garner private property and transfer the property to private buyers. The public use argument by Connecticut is that the private developers would spur economic development by constructing businesses for the local area. Susan Kelo, an individual affected by Connecticut's actions argued that the taking of the land from one private owner to another does not fit under the "public use" requirement of the Fifth Amendment. The court rejected Susan Kelo's argument and took sides with the city of New London. The Supreme Court reasoned that the construction of developmental properties would constitute a public use as the public would economically benefit from the construction.