The Constitution of the United States specifies the apportionment of seats of the House of Representatives to the various states on the basis of each state's population (for the upper chamber, the Senate, each state is apportioned exactly two seats each). The U.S. Constitution says nothing about drawing districts for the individual state legislatures.
Representatives and direct taxes shall be apportioned among the several states which may be included within this union, according to their respective numbers... [Article I, section 2]
Of course, you have to know how many people actually live in the various states, and you have to be sure to update those numbers on a periodic basis because of population changes. That's why Article I (the legislative article) of the Constitution requires that a census of the population be conducted every ten years. It states:
The actual Enumeration [of the population] shall be made within three years after the first meeting of the Congress of the United States, and within every subsequent term of ten years, in such manner as they shall by law direct. [Article I, section 2]
Despite requiring reapportionment after each decennial census of the population, the Constitution is silent on the actual process of redrawing districts for the U.S House of Representatives (or for districts for the state legislatures). Admired for its brevity and flexibility, the Constitution says this about the election of members of Congress:
The times, places and manner of holding elections for Senators and Representatives, shall be prescribed in each state by the legislature thereof; but the Congress may at any time by law make or alter such regulations, except as to the places of choosing Senators. [Article I, section 4]
It is of little wonder, then, that politicians have tried to rig the process and the outcomes of redistricting since the founding of the Republic. Indeed, the term gerrymander (drawing legislative districts to maximize political goals at the expense of all other considerations) was coined in 1812, when our new country was still in its infancy.
Over the years, particularly in the post-Civil Rights era, the U.S. Supreme Court and the Department of Justice have placed restrictions on the redrawing of congressional and legislative districts to protect the representation of racial and ethnic minorities (see minority vote concentration and minority vote dilution in the glossary). Despite these, the practice of drawing districts for political advantage has not been fundamentally challenged.