Training and/or using a recurrent neural network model for visual servoing of an end effector of a robot. In visual servoing, the model can be utilized to generate, at each of a plurality of time steps, an action prediction that represents a prediction of how the end effector should be moved to cause the end effector to move toward a target object. The model can be viewpoint invariant in that it can be utilized across a variety of robots having vision components at a variety of viewpoints and/or can be utilized for a single robot even when a viewpoint, of a vision component of the robot, is drastically altered. Moreover, the model can be trained based on a large quantity of simulated data that is based on simulator(s) performing simulated episode(s) in view of the model. One or more portions of the model can be further trained based on a relatively smaller quantity of real training data.