Deep neural networks are now rivaling human accuracy in several pattern recognition problems. Compared to traditional classifiers, where features are handcrafted, neural networks learn increasingly complex features directly from the data. Instead of handcrafting the features, it is now the network architecture that is manually engineered. The network architecture parameters such as the number of layers or the number of filters per layer and their interconnections are essential for good performance. Even though basic design guidelines exist, designing a neural network is an iterative trial-and-error process that takes days or even weeks to perform due to the large datasets used for training. In this paper, we present DeepEyes, a Progressive Visual Analytics system that supports the design of neural networks during training. We present novel visualizations, supporting the identification of layers that learned a stable set of patterns and, therefore, are of interest for a detailed analysis. The system facilitates the identification of problems, such as superfluous filters or layers, and information that is not being captured by the network. We demonstrate the effectiveness of our system through multiple use cases, showing how a trained network can be compressed, reshaped and adapted to different problems.