Visual representation of information is a fundamental tool for advancing our understanding of science. It enables the research community to extract new knowledge from complex datasets, and plays an equally vital role in communicating new results across a spectrum of public audiences. Visualizations which make research results accessible to the public have been popularized by the press, and are used in formal education, informal learning settings, and all aspects of lifelong learning. In particular, visualizations of astronomical data (hereafter astrovisualization or astroviz) have broadly captured the human imagination, and are in high demand. Astrovisualization practitioners need a wide variety of specialized skills and expertise spanning multiple disciplines (art, science, technology). As astrophysics research continues to evolve into a more data rich science, astroviz is also evolving from artists conceptions to data-driven visualizations, from two-dimensional images to three-dimensional prints, requiring new skills for development. Currently astroviz practitioners are spread throughout the country. Due to the specialized nature of the field there are seldom enough practitioners at one location to form an effective research group for the exchange of knowledge on best practices and new techniques. Because of the increasing importance of visualization in modern astrophysics, the fact that the astroviz community is small and spread out in disparate locations, and the rapidly evolving nature of this field, we argue for the creation and nurturing of an Astroviz Community of Practice. We first summarize our recommendations. We then describe the current make-up of astrovisualization practitioners, give an overview of the audiences they serve, and highlight technological considerations.