Explanations for Convolutional Neural Networks (CNNs) based on relevance of input pixels might be too unspecific to evaluate which and how input features impact model decisions. Especially in complex real-world domains like biomedicine, the presence of specific concepts (e.g., a certain type of cell) and of relations between concepts (e.g., one cell type is next to another) might be discriminative between classes (e.g., different types of tissue). Pixel relevance is not expressive enough to convey this type of information. In consequence, model evaluation is limited and relevant aspects present in the data and influencing the model decisions might be overlooked. This work presents a novel method to explain and evaluate CNN models, which uses a concept- and relation-based explainer (CoReX). It explains the predictive behavior of a model on a set of images by masking (ir-)relevant concepts from the decision-making process and by constraining relations in a learned interpretable surrogate model. We test our approach with several image data sets and CNN architectures. Results show that CoReX explanations are faithful to the CNN model in terms of predictive outcomes. We further demonstrate that CoReX is a suitable tool for evaluating CNNs supporting identification and re-classification of incorrect or ambiguous classifications.