The United States Congress cannot pass bills of attainder, suspend the writ of habeas corpus unless it is a time of national emergency or pass ex post facto laws. Even though Congress lacks these three powers, it can still accomplish a lot for the good of the country.
Bills of attainder are those bills that punish people outside of the court system. Ex post facto laws are acts that are outlawed after they have been committed. A writ of habeas corpus is a court order that requires the federal government to charge people arrested for crimes.
Both the House of Representatives and Senate have a unique set of powers. The House can impeach a federal official and propose tax bills. The Senate has the power to ratify treaties, try impeached officials, confirm federal judicial candidates and approve presidential appointments to federal positions.
Certain matters require the approval of both the House and Senate. A declaration of war must pass both houses, and both have to approve the same version of the same law to enable it to pass.
If the House impeaches an official, the impeachment doesn't take effect until the Senate has found the official guilty of the charges brought against him. For example, the House has impeached two presidents, Andrew Johnson and Bill Clinton. Both presidents got to remain in office because the Senate acquitted both men.