Transmission electron microscope tomographic data of aligned carbon nanotubes in epoxy at volume fractions of 0.44%, 2.6%, 4%, and 6.9%. Reduced data and analysis are available at https://doi.org/10.1021/acsnano.5b01044 . This is the raw data used to generate the figures in "The evolution of carbon nanotube network structure in unidirectional nanocomposites resolved by quantitative electron tomography", Bharath Natarajan, Noa Lachman, Thomas Lam, Douglas Jacobs, Christian Long, Minhua Zhao, Brian L Wardle, Renu Sharma, J Alexander Liddle, ACS Nano, vol. 9, pp 6050-6058 (2015), and is further analyzed in "Aligned carbon nanotube morphogenesis predicts physical properties of their polymer nanocomposites", Bharath Natarajan, Itai Y. Stein, Noa Lachman, Namiko Yamamoto, Douglas S. Jacobs, Renu Sharma, J. Alexander Liddle and Brian L. Wardle, Nanoscale, vol. 11, pp16327-16335 (2019), and "Modeliing the Electromagnetic Scattering Characteristics of Carbon Nanotube Composites Characterized by 3-D Tomographic Transmission Electron Microscopy", Ahmed M. Hassan, MD Khadimul Islam, Spencer On, Bharath Natarajan, Itai Y. Stein, Noa Lachman, Estelle Cohen, Brian L. Wardle, Renu Sharma, J. Alexander Liddle, and Edward J. Garboczi, IEEE Open Journal of Antennas and Propagation, vol. 1, pp 142-158 (2020). Carbon nanotube (CNT) reinforced polymers are next-generation, high-performance, multifunctional materials with a wide array of promising applications. Successful introduction of such materials is hampered by the lack of a quantitative understanding of process-structure-property relationships. These relationships are developed through the detailed characterization of nanoscale reinforcement morphology within the embedding medium. We reveal the three-dimensional (3D) nanoscale morphology of high volume fraction (Vf) aligned CNT/epoxy-matrix nanocomposites using energy-filtered electron tomography. We present an automated phase-identification method for fast, accurate, representative rendering of the CNT spatial arrangement in these low-contrast bimaterial systems. The resulting nanometer-scale visualizations provide quantitative information on the evolution of CNT morphology and dispersion state with increasing Vf, including network structure, CNT alignment, bundling and waviness. The CNTs exhibit a nonlinear increase in bundling and alignment and a decrease in waviness as a function of increasing Vf. Our findings explain previously observed discrepancies between the modeled and measured trends in bulk mechanical, electrical and thermal properties. The techniques we have developed for morphological quantitation are applicable to many low-contrast material systems. We use new, nanoscale quantitative 3D morphological information and stochastic modeling to re-interpret experimental measurements of continuous aligned carbon nanotube (A-CNT) PNC properties as a function of A-CNT packing/volume fraction. The 3D tortuosity calculated from tomographic reconstructions and its evolution with Vf is used to develop a novel definition of waviness that incorporates the stochastic nature of CNT growth. The importance of using randomly wavy CNTs to model these materials is validated by agreement between simulated and previously-measured PNC elastic moduli. Secondary morphological descriptors such as CNT-CNT junction density and inter-junction distances are measured for transport property predictions. The scaling of the junction density with CNT volume fraction is observed to be non-linear, and this non-linearity is identified as the reason behind the previously unexplained scaling of aligned-CNT PNC longitudinal thermal conductivity. The measured electrical conductivity scales linearly with Vf as it is relatively insensitive to junction density beyond percolation.