Attention is a mechanism that has been instrumental in driving remarkable performance gains of deep neural network models in a host of visual, NLP and multimodal tasks. One additional notable aspect of attention is that it conveniently exposes the “reasoning” behind each particular output generated by the model. Specifically, attention scores over input regions or intermediate features have been interpreted as a measure of the contribution of the attended element to the model inference. While the debate in regard to the interpretability of attention is still not settled, researchers have pointed out the existence of architectures and scenarios that afford a meaningful interpretation of the attention mechanism. Here we propose the generalization of attention from low-level input features to high-level concepts as a mechanism to ensure the interpretability of attention scores within a given application domain. In particular, we design the ConceptTransformer, a deep learning module that exposes explanations of the output of a model in which it is embedded in terms of attention over user-defined high-level concepts. Such explanations are plausible (i.e. convincing to the human user) and faithful (i.e. truly reflective of the reasoning process of the model). Plausibility of such explanations is obtained by construction by training the attention heads to conform with known relations between inputs, concepts and outputs dictated by domain knowledge. Faithfulness is achieved by design by enforcing a linear relation between the transformer value vectors that represent the concepts and their contribution to the classification log-probabilities. We validate our CT module on established explainability benchmarks and show how it can be used to infuse domain knowledge into classifiers to improve accuracy, and conversely to extract concept-based explanations of classification outputs.