As for nanofillers in general, the properties of carbon nanotube (CNT) -polymer composites depend strongly on the filler arrangement and the structure of the filler network. This article reviews our actual understanding of the relation between processing conditions, state of CNT dispersion and structure of the filler network on the one hand, and the resulting electrical, melt rheological and mechanical properties, on the other hand. The as-produced rather compact agglomerates of CNTs (initial agglomerates, >1 µm), whose structure can vary for different tube manufacturers, synthesis and/or purification conditions, have first to be well dispersed in the polymer matrix during the mixing step, before they can be arranged to a filler network with defined physical properties by forming secondary agglomerates. Influencing factors on the melt dispersion of initial agglomerates of multi-walled CNTs into individualized tubes are discussed in context of dispersion mechanisms, namely the melt infiltration into initial agglomerates, agglomerate rupture and nanotube erosion from agglomerate surfaces. The hierarchical morphology of filler arrangement resulting from secondary agglomeration processes has been found to be due to a competition of build-up and destruction for the actual melt temperature and the given external flow field forces. Related experimental results from in-line and laboratory experiments and a model approach for description of shear-induced properties are presented