Deep learning has undoubtedly offered tremendous improvements in the performance of state-of-the-art speech emotion recognition (SER) systems. However, recent research on adversarial examples poses enormous challenges on the robustness of SER systems by showing the susceptibility of deep neural networks to adversarial examples as they rely only on small and imperceptible perturbations. In this study, we evaluate how adversarial examples can be used to attack SER systems and propose the first black-box adversarial attack on SER systems. We also explore potential defenses including adversarial training and generative adversarial network (GAN) to enhance robustness. Experimental evaluations suggest various interesting aspects of the effective utilization of adversarial examples useful for achieving robustness for SER systems opening up opportunities for researchers to further innovate in this space.