A carbon nanotube (CNT) sheet containing CNTs having a median length of at least 0.05 mm and an aspect ratio of at least 2,500; L arranged b a randomly oriented, uniformly distributed pattern, and having a basis weight of at least 1 gsm and a relative density of less than 1.0. The CNT sheet is manufactured by applying a CNT suspension in a continuous pool over a filter material to a depth sufficient to prevent puddling of the CNT suspension upon the surface of the •filter material, and drawing the dispersing liquid through the filter material to provide a uniform CNT dispersion and form the CNT sheet. The CNT sheet is useful in making CNT composite laminates and structures having utility for electromagnetic wave absorption, lightning strike dissipation. EMI shielding, thermal interface pads, energy storage, and heat dissipation.