The high capacity of neural networks allows fitting models to data with high precision, but makes generalization to unseen data a challenge. If a domain shift exists, i.e. differences in image statistics between training and test data, care needs to be taken to ensure reliable deployment in real-world scenarios. In digital pathology, domain shift can be manifested in differences between whole-slide images, introduced by for example differences in acquisition pipeline - between medical centers or over time. In order to harness the great potential presented by deep learning in histopathology, and ensure consistent model behavior, we need a deeper understanding of domain shift and its consequences, such that a model's predictions on new data can be trusted. This work focuses on the internal representation learned by trained convolutional neural networks, and shows how this can be used to formulate a novel measure - the representation shift - for quantifying the magnitude of model-specific domain shift. We perform a study on domain shift in tumor classification of hematoxylin and eosin stained images, by considering different datasets, models, and techniques for preparing data in order to reduce the domain shift. The results show how the proposed measure has a high correlation with drop in performance when testing a model across a large number of different types of domain shifts, and how it improves on existing techniques for measuring data shift and uncertainty. The proposed measure can reveal how sensitive a model is to domain variations, and can be used to detect new data that a model will have problems generalizing to. We see techniques for measuring, understanding and overcoming the domain shift as a crucial step towards reliable use of deep learning in the future clinical pathology applications.