For robots to become valuable assistants in real-world scenarios, they must effectively manipulate unknown objects in complex environments, such as homes with multiple objects on shelves or desks. A critical aspect of manipulating objects is grasping them with the robot’s end-effector. The key challenge for grasping an unknown object lies in determining how to position and orientate the end-effector relative to the object. While prior research has predominantly focused on tabletop scenarios with fixed camera-workspace transforms, in this thesis, we extend robotic grasping to domestic settings. This thesis makes three principal contributions in this area: (i) extending a depthimage- based grasp quality prediction method to accommodate 6-DoF grasps and versatile camera poses, (ii) creating a depth-image-based grasp proposal method tailored for 6-DoF grasps and unknown camera-workspace transforms, and (iii) applying such a grasp proposal method in complex, domestic environments. For application in domestic environments, we develop a simulation pipeline specifically designed for training and evaluating grasp proposal models in domestic settings. Quantitative experiments demonstrate competitive or superior performance of our approach when compared with widely used techniques across a number of challenging simulated experiments. Additionally, real-world experiments with a mobile manipulator demonstrate successful grasping of unknown objects positioned on tables and shelves in unknown poses. We make our code and pre-trained models available for fellow researchers, facilitating the direct application of our models when attempting to grasp unknown objects with mobile manipulators in domestic environments.