In recent decades, robotics has attracted more and more attention from researchers since they have been widely used in scientific researches and engineering applications, such as space exploration, under water survey, industrial and military industries, welding, painting and assembly, and medical applications, and so on [1,2]. Much effort has been contributed to robotics, and different types of robot manipulators have thus been developed and investigated, such as serial manipulators consist of redundant manipulators [3] and mobile manipulators [4], parallel manipulators [5], and cable-driven manipulators [6]. A redundant manipulator is often designed as a series of links connected by motor-actuated joints that extends from a fixed base to an end-effector while a mobile manipulator is often designed as a robotic device composed of a mobile platform and a redundant manipulator fixed to the platform [7]. Different from these serial manipulators, a parallel manipulator is a mechanical system that usually uses several serial chains to support a single platform, or end-effector. Besides, a cable-driven manipulator is a special parallel manipulator, in which the moving platform is driven by cables instead of rigid links [8]. Using these manipulators to save labors and increase accuracies are becoming common practices in various industrial fields. As a consequence, many approaches have been proposed, investigated and employed for the control of robot manipulators [9]. Among them, thanks to many advantages in parallel distributed structure, nonlinear mapping, ability to learn from examples, high generalization performance, and capability to approximate an arbitrary function with sufficient number of neurons, the neural-network-based approach is a competitive way to control movements of robot manipulators [1]. Generally speaking, neural networks can be classified into different types according to different criterions. For example, in terms of the structure of the network, they can be classified into two categories: feedforward neural networks and recurrent neural networks [10,11]. A feedforward neural network is an artificial neural network with no cycles or feedback signal inside while a recurrent neural network allows bi-directional information flow, which means the information inside flows from a successive node to a previous one (or called feedback) or forms a closed cycle within a single node. In this paper, we make a relatively comprehensive review of research progress on controlling these robot manipulators by means of neural networks. The overall organization of the paper is as follows. After the introduction, we present preliminaries on the control of robot manipulators based on neural networks in Section 2. Section 3 presents and reviews different types of robot manipulators in detail with the corresponding schematics being illustrated. In addition, Section 4 revisits applications of different neural networks to the control of robot manipulators. Moreover, two possible future research directions on control of robot manipulators using neural networks are pointed out in Section 5. Finally, Section 6 concludes the paper with final remarks.