We describe how networks based on information theory can help measure and visualize systemic risk, enhance diversification, and help price assets. To do this, we first define a distance measure based on the mutual information between asset pairs and use this measure in the construction of minimum spanning trees. The dynamics of the shape and the descriptive statistics of these trees are analyzed in various investment domains. The method provides evidence of regime changes in dependency structures prior to market sell-offs and, as such, it is a potential candidate for monitoring systemic risk. We also provide empirical evidence that the assets that are located toward the center of the network tend to have higher returns. Finally, an investment strategy that utilizes network centrality information is shown to add value historically.