We believe that mobile devices offer great, only partly realized, potential in the context of both personal and professional information visualization. In this position paper, we outline three important and promising aspects of information visualization with mobile devices: the development of a consistent multi-touch interaction framework that can be applied to a variety of visualization techniques; the combination of common touch input with advanced spatial input techniques; and the usage of the spatial arrangement of multiple, co-located mobile devices. We explore these aspects by highlighting important questions and major challenges. Furthermore, we present several approaches and early concepts which illustrate our ongoing investigations in this field of research.