BADGr -A toolbox for Box-based Approximation, Decomposition and GRasping. In this paper, we conclude our work on shape approximation by box primitives for the goal of simple and efficient grasping. As a main product of our research, we present the BADGr toolbox for Box-based Approximation, Decomposition and Grasping of objects. The contributions of the work presented here are twofold: in terms of shape approximation, we provide an algorithm for creating a 3D box primitive representation to identify object parts from 3D point clouds. We motivate and evaluate this choice particularly towards the task of grasping. As a contribution in the field of grasping, we further provide a grasp hypothesis generation framework that utilizes the chosen box presentation in a flexible manner.