The short answer to this question is; the state legislature. In regard to congressional districts, Article 1, Sec. 4 of the U.S. Constitution gives states the authority to determine the “times, places and manner of holding [federal] elections.” Congress may override states regarding this, but it has historically declined to do so. In addition, state legislatures have authority over redistricting its own legislative lines unless the state's constitution directs otherwise or if the legislature has delegated that duty to another entity. (“[S]tate legislatures have ‘primary jurisdiction’ over legislative reapportionment.” White v. Weiser, 412 U.S. 783, 795 (1973).

There are various entities that states use to replace the traditional role of the legislature in redistricting, but in most states redistricting remains the province of the legislature. In the past, reform-minded groups have used Iowa as a good example of how politics could be taken out of redistricting, with its use of nonpartisan staff to draw redistricting maps. However, the Iowa legislature retains control over the mapmaking, since the legislature may reject the maps. In Arkansas, the Board of Apportionment is responsible for redrawing the states’ legislative districts. The Board consists of the governor, the secretary of state, and the attorney general.

In the past two decades, commissions have become a popular reform for redistricting however, commissions refer to a large array of redistricting entities, some of which are substantially controlled by the legislature and/or executive branch or have no decision-making power.  Because of this, it is important to distinguish truly “independent” or “citizen” commissions from those entities that are heavily influenced by the legislature. A list of commission websites is here.

Whether commission members are influenced by legislature generally depends on the method of selecting commission members and whether there are restrictions on who may serve on the body. For example, some bipartisan commissions are appointed by legislative leaders and may consist of legislators or other public officials. Independent commissions on the other hand, go through either a randomized or other objective selection process (usually by a nonpartisan entity) and may prohibit members affiliated with the legislature or any public office. It is also important to note that many commissions may only have authority over one map as opposed to both congressional and legislative districts.

To determine to what degree a commission is independent of the legislature, you must consider whether the commission; 1) has exclusive power to enact a map; 2) is comprised of appointed members, or members selected via a nonpartisan process; and 3) excludes candidates affiliated with the legislature, political party officials, individuals who hold or recently held public office, or lobbyists.