Grasping is the process of picking up an object by applying forces and torques at a set of contacts. Recent advances in deep learning methods have allowed rapid progress in robotic object grasping. In this systematic review, we surveyed the publications over the last decade, with a particular interest in grasping an object using all six degrees of freedom of the end-effector pose. Our review found four common methodologies for robotic grasping: sampling-based approaches, direct regression, reinforcement learning, and exemplar approaches In addition, we found two “supporting methods” around grasping that use deep learning to support the grasping process, shape approximation, and affordances. We have distilled the publications found in this systematic review (85 papers) into ten key takeaways we consider crucial for future robotic grasping and manipulation research.