In contrast to the cases of single particle Schrödinger operators and ideal Bose gases the effects of random external potentials on many-body systems of interacting particles is still poorly understood. In the lecture the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons, where a fairly complete picture can be established in a suitable limit, will be discussed. This is joint work with Robert Seiringer and Valentin Zagrebnov.