Robotic manipulators are highly valuable tools that have become widespread in the industry, as they can achieve great precision and velocity in pick and place as well as processing tasks. However, to unlock their complete potential, some problems such as inverse kinematics (IK) need to be solved: given a Cartesian target, a method is needed to find the right configuration for the robot to reach that point. Another issue that needs to be addressed when dealing with robotic manipulators is the obstacle avoidance problem. Workspaces are usually cluttered and the manipulator should be able to avoid colliding with objects that could damage it, as well as with itself. Two alternatives exist to do this: a controller can be designed that computes the best action for each moment given the manipulator’s state, or a sequence of movements can be planned to be executed by the robot. Classical approaches to all these problems, such as numeric or analytical methods, can produce precise results but take a high computation time and do not always converge. Learning-based methods have gained considerable attention in tackling the IK problem, as well as motion planning and control. These methods can reduce the computational cost and provide results for every situation avoiding singularities. This article presents a literature review of the advances made in the past five years in the use of Deep Neural Networks (DNN) for IK with regard to control and planning with and without obstacles for rigid robotic manipulators. The literature has been organized in several categories depending on the type of DNN used to solve the problem. The main contributions of each reference are reviewed and the best results are presented in summary tables.