Recent studies have shown that deep learning algorithms used for image classification or object recognition are not sufficiently reliable. These algorithms can be easily fooled by applying perturbations to images or generating artificial images that result in misclassification. In this paper, we provide an overview of software testing methods present in literature to test deep learning systems. We have explored different methods of testing deep neural networks, namely metamorphic testing, mutation testing, differential testing, and adversarial perturbation testing. We present the main findings available from the literature and compare these methods systematically and comprehensively. The results show that systematic testing of deep learning systems can further help to increase the performance of state-of-the-art systems.