After decades of digitization, large cultural heritage collections have emerged on the web, which contain massive stocks of content from galleries, libraries, archives, and museums. This increase in digital cultural heritage data promises new modes of analysis and increased levels of access for academic scholars and casual users alike. Going beyond the standard representations of search-centric and grid-based interfaces, a multitude of approaches has recently started to enable visual access to cultural collections, and to explore them as complex and comprehensive information spaces by the means of interactive visualizations. In contrast to conventional web interfaces, we witness a widening spectrum of innovative visualization types specially designed for rich collections from the cultural heritage sector. This new class of information visualizations gives rise to a notable diversity of interaction and representation techniques while lending currency and urgency to a discussion about principles such as serendipity, generosity, and criticality in connection with visualization design. With this survey, we review information visualization approaches to digital cultural heritage collections and reflect on the state of the art in techniques and design choices. We contextualize our survey with humanist perspectives on the field and point out opportunities for future research.