Depending on their structure and order (individual, films, bundled, buckypapers, etc.), carbon nanotubes (CNTs) demonstrate different values of thermal conductivity, from the level of thermal insulation with the thermal conductivity of 0.1 W/mK to such high values as 6600 W/mK. This review article concentrates on analyzing the articles on thermal conductivity of CNT networks. It describes various measurement methods, such as the 3-omega method, bolometric, steady-state method and their variations, hot-disk method, laser flash analysis, thermoreflectance method and Raman spectroscopy, and summarizes the results obtained using those techniques. The article provides the main factors affecting the value of thermal conductivity, such as CNT density, number of defects in their structure, CNT ordering within arrays, direction of measurement in relation to their length, temperature of measurement and type of CNTs. The practical methods of using CNT networks and the potential directions of future research in that scope were also described.