  The multiloop amplitudes for open bosonic string in 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 non--trivially only the
zero modes. This makes it possible to write in a simple and elegant way the
general expression for multiloop string amplitudes in 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.
