Every visualization researcher and practitioner knows the painful experience of a beautifully designed network layout breaking down once the input graph scales up to realistic node and edge counts. The resulting "hairball" suffers from cluttering and over-plotting to an extreme that renders it unusable for any practical purposes. Since researchers have had this experience for decades, various approaches have been developed on all stages of the visualization pipeline to alleviate this problem. They range from filtering and clustering techniques on the data level to modern GPU-based techniques on the image level. This tutorial gives an overview of these techniques and discusses their applicability and interplay in different application scenarios. By doing so, it provides a unique problem-oriented perspective on the field of scalable network visualization, which is an area of active research today more than ever. The tutorial serves mainly to further the understanding of network visualization beyond the point of creating an initial layout. It thus caters to an intermediate level audience with some basic knowledge on graph layout and visualization, but it will certainly present an interesting cross-section through the larger domains of network visualization and graph drawing for established researchers as well.