This study surveys the state of the art in usability and user experience strategies applied to applications that deal with large amounts of data in the field of cultural heritage, highlighting the most prominent aspects and underlining the under-explored. In these applications, large amounts of data need to be wisely presented to help final users at drawing conclusions and making decisions. While sophisticated technology may be used to improve the user experience, it should not be applied to the detriment of usability, which is critical for the success of these applications. We performed a systematic mapping study to classify the literature retrieved in the four largest scientific databases by a structured search string. We classify applications according to purpose, intended users, the way they address and evaluate user experience and usability, among others, and include the analysis of combined results through maps. Findings reveal the contradiction that while most articles are intended for the education and tourism of the general public, only half of the studies evaluate usability. Moreover, there is a significant research gap in user interfaces for systems in the context of preventive conservation, for research, assessment and decision assistance. This is the first systematic mapping study combining usability and cultural heritage, especially for data-oriented applications. It shows that more research is necessary to assist conservators and researchers and to address usability from early stages of development.