Most notably in the work of J.L. Moreno (1934), visual representations have long beena means of both presentation and exploration of social structures.  To create effective network visualizations, three main aspects have to be considered: the substance (data, interest, context, derived data), a design (mapping substance to graphical elements and variables), and algorithms (that are to realize a design without introducing artifacts obscuring the information).  For selected substantive categories, I present historical and current examples of visualizations and point out open algorithmic issues associated with them.  I conclude with more broadly defined challenges that are based on recurrent problems in social network analysis.