Recent advances in generalized image understanding have seen a surge in the use of deep convolutional neural networks (CNN) across a broad range of image-based detection, classification and prediction tasks. Whilst the reported performance of these approaches is impressive, this paper investigates the hitherto unapproached question of the impact of commonplace image and video compression techniques on the performance of such deep learning architectures. Focusing on the JPEG and H.264 (MPEG-4 AVC) as a representative proxy for contemporary lossy image/video compression techniques that are in common use within network-connected image/video devices and infrastructure, we examine the impact performance across five discrete tasks: human pose estimation, semantic segmentation, object detection, action recognition, and monocular depth estimation. As such, within this study we include a variety of network architectures and genres spanning end-to-end convolution, encoder-decoder, region-based CNN (R-CNN), dual-stream, and generative adversarial networks (GAN). Our results show a non-linear and non-uniform relationship between network performance and the level of lossy compression applied. Notably, performance decreases significantly below a JPEG quality (quantization) level of 15% and a H.264 Constant Rate Factor (CRF) of 40. However, re-training said architectures on pre-compressed imagery conversely recovers network performance by up to 78.4% in some cases. Furthermore, there is a correlation between architectures employing an encoder-decoder pipeline and those that demonstrate resilience to lossy image compression. The characteristics of this input compression to output performance impact can be used to inform design decisions within future image/video devices and infrastructure.