This presentation seeks to provide a big picture overview of network methods for the purpose of identifying and visualizing connections between different variables with a specific focus on extreme events. We start with a quick overview of traditional climate networks - such as correlation networks - and explain why those may not be suitable to analyze extremal dependence. Next, we review a type of climate network which is suitable for this purpose, namely event synchronization networks. We then look at the new concept of chi-networks, introduced in the first presentation of this session. Finally, we put the latter two types of networks in context of each other through the use of a proposed building block language, which can be used to identify similarities and differences between chi-networks and event synchronization networks, and to generate yet other network types for the analysis of extremes.