A complete literature review of carbon nanotube (CNT) yarn conductivities is presented, highlighting that CNT yarns made from CNT arrays grown by Chemical Vapor Deposition show a resistivity limitation of around 1 mΩ cm. We bring a deep understanding of the conduction limitation in CNT yarns spun from arrays thanks to systematic electrical transport studies in a large temperature range (3 K - 350 K) in CNT yarns made in different conditions of densification, doping and CNT lengths. The analysis of the electrical transport by the reduced activation energy clearly uncouples the effects of the inter-CNT contacts, prevailing below 70 K and the intrinsic CNT resistivity (prevailing above 70 K). Contrary to what is commonly accepted, we show that the contacts between CNTs have no impact on the CNT yarn resistivity at room temperature. In addition, we present a unique study of the structural and electrical properties of the CNT web which reveals that the CNT bundles are very well connected with each other. We estimate the CNT bundle resistivity (0.8 mΩ cm) to be close to that of the CNT yarn (1.1 mΩ cm). We conclude that, at room temperature, the CNT yarn resistivity is limited by that of the CNT bundle.