Multilayer carbon nanotube capacitors, and methods and printable compositions for manufacturing multilayer carbon nanotubes (CNTs) are disclosed. A first capacitor embodiment includes: a first conductor; a plurality of fixed CNTs in an ionic liquid, each fixed CNT comprising a magnetic catalyst nanoparticle coupled to a carbon nanotube and further coupled to the first conductor; and a first plurality of free CNTs dispersed and moveable in the ionic liquid. Another capacitor embodiment includes: a first conductor; a conductive nanomesh coupled to the first conductor; a first plurality of fixed CNTs in an ionic liquid and further coupled to the conductive nanomesh; and a plurality of free CNTs dispersed and moveable in the ionic liquid. Various methods of printing the CNTs and other structures, and methods of aligning and moving the CNTs using applied electric and magnetic fields, are also disclosed.