Enumerated powers are the specific responsibilities granted to the U.S. Congress by the U.S. Constitution. They are found in Article 1 Section 8 of the Constitution.
Congress can only exercise the powers that the Constitution allows. Other powers are limited by the Bill of Rights, and the Constitution itself provides other protections. Several clauses and the 10th amendment deal with the enumerated powers.
The Necessary and Proper Clause of Article 1 Section 8 has been controversial since the early days of the United States. Depending on interpretation, it can be used to expand the powers of Congress or limit those powers. It has been used mostly, along with the Commerce Clause, to provide a constitutional basis for many new laws.
The section's Commerce Clause has been used to pass many laws on human behavior that are not mentioned in the Constitution. The Supreme Court has generally upheld this assertion over the years. The court believes that many behaviors can have an effect on interstate commerce.
The 10th Amendment is often cited to maintain that Congress does not have the right to pass any law that its members believe it should. Courts often disagree, using the Commerce Clause to trump many arguments that the 10th Amendment should substantially limit the powers that Congress holds.