Which powers are granted to Congress by the Constitution?

In Article I of the Constitution are listed the powers granted to Congress.  Generally, Congress is empowered to create all legislation for the United States. This is stated in the first section of the article.  The subject matters of this legislation, what are often called the enumerated powers, are listed in Section 8 and in various amendments, and these cover a broad range.

Congress can legislate to impose taxes, provide for the payment of debt...

In Article I of the Constitution are listed the powers granted to Congress.  Generally, Congress is empowered to create all legislation for the United States. This is stated in the first section of the article.  The subject matters of this legislation, what are often called the enumerated powers, are listed in Section 8 and in various amendments, and these cover a broad range.

Congress can legislate to impose taxes, provide for the payment of debt and for incurring debt, and for payment for the defense of the country. It may legislate on any matter affecting interstate commerce and on commerce with native Americans and other countries. It is the sole body that can create bankruptcy law.  It is responsible for legislation on immigration and naturalization.  It is responsible for coining money, that is to say, for its production and value, as well as for what punishments ensue for counterfeiting American money. The postal system is a creature of Congress, which established its enabling legislation and continues to control it to this day.  Patent and copyright law are the responsibility of Congress.  While the Constitution establishes the Supreme Court of the United States, all other lower courts are established by Congress through legislation. This includes the federal district and circuit courts.  Congress legislates to establish maritime law, which is the law of the sea. Its military powers are broad, to declare war, to create military entities and to fund then, and to create the rules that govern those military entities. An army and navy are mentioned specifically, but of course, there was no air force when the Constitution was created. Also part of this group of powers is the power to create and call forth the state militias, which we now refer to as the National Guard.  Congress also has complete legislative authority over Washington, D.C., which is not a state at all, but the center of federal government. Additionally, each time an amendment has been passed that required some legislative authority, included within the amendment is the granting of power to Congress to enforce that amendment through legislation. 

Any power that is not enumerated in the Constitution and its amendments is a power that falls to the states. This is why most criminal law, family law, and negligence law, to name a few examples, are created by state legislatures, and why there is variability in these areas from one state to another.