The application of Deep Neural Networks (DNNs) to a broad variety of tasks demands methods for coping with the complex and opaque nature of these architectures. When a gold standard is available, performance assessment treats the DNN as a black box and computes standard metrics based on the comparison of the predictions with the ground truth. A deeper understanding of performances requires going beyond such evaluation metrics to diagnose the model behavior and the prediction errors. This goal can be pursued in two complementary ways. On one side, model interpretation techniques "open the box" and assess the relationship between the input, the inner layers and the output, so as to identify the architecture modules most likely to cause the performance loss. On the other hand, black-box error diagnosis techniques study the correlation between the model response and some properties of the input not used for training, so as to identify the features of the inputs that make the model fail. Both approaches give hints on how to improve the architecture and/or the training process. This paper focuses on the application of DNNs to Computer Vision (CV) tasks and presents a survey of the tools that support the black-box performance diagnosis paradigm. It illustrates the features and gaps of the current proposals, discusses the relevant research directions and provides a brief overview of the diagnosis tools in sectors other than CV.