Omnidirectional (or 360-degree) images and videos are emergent signals in many areas such as robotics and virtual/augmented reality. In particular, for virtual reality, they allow an immersive experience in which the user is provided with a 360-degree field of view and can navigate throughout a scene, e.g., through the use of Head Mounted Displays. Since it represents the full 360-degree field of view from one point of the scene, omnidirectional content is naturally represented as spherical visual signals. Current approaches for capturing, processing, delivering, and displaying 360-degree content, however, present many open technical challenges and introduce several types of distortions in these visual signals. Some of the distortions are specific to the nature of 360-degree images, and often different from those encountered in the classical image communication framework. This paper provides a first comprehensive review of the most common visual distortions that alter 360-degree signals undergoing state of the art processing in common applications. While their impact on viewers' visual perception and on the immersive experience at large is still unknown ---thus, it stays an open research topic--- this review serves the purpose of identifying the main causes of visual distortions in the end-to-end 360-degree content distribution pipeline. It is essential as a basis for benchmarking different processing techniques, allowing the effective design of new algorithms and applications. It is also necessary to the deployment of proper psychovisual studies to characterise the human perception of these new images in interactive and immersive applications.