Most stars with the mass of the sun or larger have one or more companion stars, but when and how these multiple stars form is one of the controversial central problems of astronomy. Gravity contracts the natal gas and dust in an interstellar cloud until clumps develop that are dense enough to coalesce into stars, but how are multiple stars fashioned? Because the shrinking cloud has a slight spin, a disk (possibly a preplanetary system) eventually forms. In one model of binary star formation, this disk fragments due to gravitational instabilities, producing a second star. The other model argues that turbulence in the contracting cloud itself fragments the clumps into multiple star systems. In the first case, simulations show that the two stars should be relatively close together, typically less than about 600 astronomical units (one AU is the average distance of the earth from the sun). If the second mechanism is correct, both close and wide binary pairs can form. A distinguishing feature of the turbulent fragmentation process, and one that facilitates an observational test, is that the seeds for multiplicity are produced early in the pre-stellar phases.