Individual carbon nanotubes are like minute bits of string, and many trillions of these invisible strings must be assembled to make useful macroscopic articles. We demonstrated such assembly at rates above 7 meters per minute by cooperatively rotating carbon nanotubes in vertically oriented nanotube arrays (forests) and made 5-centimeter-wide, meter-long transparent sheets. These self-supporting nanotube sheets are initially formed as a highly anisotropic electronically conducting aerogel that can be densified into strong sheets that are as thin as 50 nanometers. The measured gravimetric strength of orthogonally oriented sheet arrays exceeds that of sheets of high-strength steel. These nanotube sheets have been used in laboratory demonstrations for the microwave bonding of plastics and for making transparent, highly elastomeric electrodes; planar sources of polarized broad-band radiation; conducting appliqués; and flexible organic light-emitting diodes.