Damages are inevitable in structures and effective damage detection techniques are important for maintaining their health. Many weight-sensitive engineering applications use composite materials, especially fiber-reinforced laminates. Common damages of these materials include delamination, fiber breakage, fiber pull-out, etc. Various non-destructive testing (NDT) techniques are reported in the literature for damage detection in composites, such as ultrasonic testing, vibration-based techniques, acoustic emission technique, optical NDT and imagining techniques. However, due to the complex properties of composite materials, conventional techniques for analyzing NDT data are difficult to implement. In this context, artificial neural network (ANN) technique is a promising alternative for analyzing NDT data for damage detection. In this study, an attempt is made to explore the state-of-the-art of damage detection in composites using NDT aided by ANN. The work discusses the pros and cons of different methods and is expected to help in identifying the appropriate method for damage detection in composites.