A carbon nanotube (CNT) sheet containing CNTs, arranged is a randomly oriented, uniformly distributed pattern, and having a basis weight of at least 1 gsm and a relative density of less than 1.5. 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 electro-thermal heating, electromagnetic wave absorption, lightning strike dissipation, EMI shielding, thermal interface pads, energy storage, and heat dissipation.