What are the restrictions placed upon congress power to legislate?

The House of Representatives and the Senate must jointly decide to exercise most of the powers granted to Congress. When Congress declares war, for example, both houses must pass the exact same declaration. Similarly, both houses must pass identical versions of the same law before the law can take effect.

Also by Article I, Section 9, Congress cannot;

Pass Ex Post Facto Laws, which outlaw acts after they have already been committed.

Pass Bills Of Attainder, which punish individuals outside of the court system.

Suspend the Writ Of Habeas Corpus, a court order requiring the federal government to charge individuals arrested for crimes. Congress can only suspend the writ of habeas corpus during times of national emergency.