The present disclosure describes carbon nanotube arrays having carbon nanotubes grown directly on a substrate and methods for making such carbon nanotube arrays. In various embodiments, the carbon nanotubes may be covalently bonded to the substrate by nanotube carbon-substrate covalent bonds. The present carbon nanotube arrays may be grown on substrates that are not typically conducive to carbon nanotube growth by conventional carbon nanotube growth methods. For example, the carbon nanotube arrays of the present disclosure may be grown on carbon substrates including carbon foil, carbon fibers and diamond. Methods for growing carbon nanotubes include a) providing a substrate, b) depositing a catalyst layer on the substrate, c) depositing an insulating layer on the catalyst layer, and d) growing carbon nanotubes on the substrate. Various uses for the carbon nanotube arrays are contemplated herein including, for example, electronic device and polymer composite applications.