In this paper three types of visualization scenarios are discussed, where topology improves the readability of particular visualization results. The first type combines topology information represented by simple graphical primitives with other forms of visual representations. The second type uses the topology information to define the relevance of objects within the data. The relevance is reflected in the visualization by applying the cut-away concept. The third type of visualizations is based on the change of topology of the underlying data to increase visibility of the most interesting information. Every type handles topology in a different way. This illustrates various roles of topology in scientific visualization.