Much of the data generated and analyzed in the life sciences can be interpreted and represented by networks or graphs. Network analysis and visualization methods help in investigating them, and many universal as well as specialpurpose tools and libraries are available for this task. However, the two fields of graph drawing and network biology are still largely disconnected. Hence, visualization of biological networks does typically not apply state-of-the-art graph drawing techniques, and graph drawing tools do not respect the drawing conventions of the life science community. In this paper, we analyze some of the major problems arising in biological network visualization. We characterize these problems and formulate a series of open graph drawing problems. These use cases illustrate the need for efficient algorithms to present, explore, evaluate, and compare biological network data. For each use case, problems are discussed and possible solutions suggested.