Information visualization is an interdisciplinary research area in which cartographic efforts have mostly addressed the handling of geographic information. Some cartographers have recently become involved in attempts to extend geographic principles and cartographic techniques to the visualization of non-geographic information. This paper reports on current progress and future opportunities in this emerging research field commonly known as spatialization. The discussion is mainly devoted to the computational techniques that turn high-dimensional data into visualizations via processes of projection and transformation. It is argued that cartographically informed engagement of computationally intensive techniques can help to provide richer and less opaque information visualizations. The discussion of spatialization methods is linked to another priority area of cartographic involvement, the development of theory and principles for cognitively plausible spatialization. The paper distinguishes two equally important sets of challenges for cartographic success in spatialization research. One is the recognition that there are distinct advantages to applying a cartographic perspective in information visualization. This requires our community to more thoroughly understand the essence of cartographic activity and to explore the implications of its metaphoric transfer to non-geographic domains. Another challenge lies in cartographers becoming a more integral part of the information visualization community and actively engaging its constituent research fields.