Abstract
The multiloop amplitudes for open bosonic string in the presence of a constant B-field are derived from first principles. The basic ingredients of the construction are the commutation relations for the string modes and the Reggeon vertex describing the interaction among three generic string states. The modifications due to the presence of the B-field affect nontrivially only the zero modes. This makes it possible to write in a simple and elegant way the general expression for multiloop string amplitudes in the presence of a constant B-field. The field theory limit of these string amplitudes is also considered. We show that it reproduces exactly the Feynman diagrams of noncommutative field theories. Issues of uv/ir are briefly discussed.