The examination of biopsy samples plays a central role in the diagnosis and staging of numerous diseases, including most cancer types. However, because of the large size of the acquired images, the localization and quantification of diseased portions of a tissue is usually time-consuming, as pathologists must scroll through the whole slide to look for objects of interest which are often only scarcely distributed. In this work, we introduce an approach to facilitate the visual inspection of large digital histopathological slides. Our method builds on a random forest classifier trained to segment the structures sought by the pathologist. However, moving beyond the pixelwise segmentation task, our main contribution is an interactive exploration framework including: (i) a region scoring function which is used to rank and sequentially display regions of interest to the user, and (ii) a relevance feedback capability which leverages human annotations collected on each suggested region. Thereby, an online domain adaptation of the learned pixelwise segmentation model is performed, so that the region scores adapt on-the-fly to possible discrepancies between the original training data and the slide at hand. Three real-time update strategies are compared, including a novel approach based on online gradient descent which supports faster user interaction than an accurate delineation of objects. Our method is evaluated on the task of extramedullary hematopoiesis quantification within mouse liver slides. We assess quantitatively the retrieval abilities of our approach and the benefit of the interactive adaptation scheme. Moreover, we demonstrate the possibility of extrapolating, after a partial exploration of the slide, the surface covered by hematopoietic cells within the whole tissue.