Robotic manipulation refers to how robots intelligently interact with the objects in their surroundings, such as grasping and carrying an object from one place to another. Dexterous manipulating skills enable robots to assist humans in accomplishing various tasks that might be too dangerous or difficult to do. This requires robots to intelligently plan and control the actions of their hands and arms. Object manipulation is a vital skill in several robotic tasks. However, it poses a challenge to robotics. The motivation behind this review paper is to review and analyze the most relevant studies on learning-based object manipulation in clutter. Unlike other reviews, this review paper provides valuable insights into the manipulation of objects using deep reinforcement learning (deep RL) in dense clutter. Various studies are examined by surveying existing literature and investigating various aspects, namely, the intended applications, the techniques applied, the challenges faced by researchers, and the recommendations adopted to overcome these obstacles. In this review, we divide deep RL-based robotic manipulation tasks in cluttered environments into three categories, namely, object removal, assembly and rearrangement, and object retrieval and singulation tasks. We then discuss the challenges and potential prospects of object manipulation in clutter. The findings of this review are intended to assist in establishing important guidelines and directions for academics and researchers in the future.