This article presents a literature review of the past five years of studies using Deep Reinforcement Learning (DRL) and Inverse Reinforcement Learning (IRL) in robotic manipulation tasks. The reviewed articles are examined in various categories, including DRL and IRL for perception, assembly, manipulation with uncertain rewards, multitasking, transfer learning, multimodal, and Human-Robot Interaction (HRI). The articles are summarized in terms of the main contributions, methods, challenges, and highlights of the latest and relevant studies using DRL and IRL for robotic manipulation. Additionally, summary tables regarding the problem and solution are presented. The literature review then focuses on the concepts of trustworthy AI, interpretable AI, and explainable AI (XAI) in the context of robotic manipulation. Moreover, this review provides a resource for future research on DRL/IRL in trustworthy robotic manipulation.