Context plays a crucial role in visual recognition as it provides complementary clues for different learning tasks including image classification and annotation. As the performances of these tasks are currently reaching a plateau, any extra knowledge, including context, should be leveraged in order to seek significant leaps in these performances. In the particular scenario of kernel machines, context-aware kernel design aims at learning positive semi-definite similarity functions which return high values not only when data share similar contents, but also similar structures (a.k.a. contexts). However, the use of context in kernel design has not been fully explored; indeed, context in these solutions is handcrafted instead of being learned. In this paper, we introduce a novel deep network architecture that learns context in kernel design. This architecture is fully determined by the solution of an objective function mixing a content term that captures the intrinsic similarity between data, a context criterion which models their structure and a regularization term that helps designing smooth kernel network representations. The solution of this objective function defines a particular deep network architecture whose parameters correspond to different variants of learned contexts including layerwise, stationary and classwise; larger values of these parameters correspond to the most influencing contextual relationships between data. Extensive experiments conducted on the challenging ImageCLEF Photo Annotation, Corel5k and NUS-WIDE benchmarks show that our deep context networks are highly effective for image classification and the learned contexts further enhance the performance of image annotation.