Examples described include composite nanofibers sheets that have been “infiltrated” with a polymer (i.e., the polymer has flowed past a surface of the nanofiber sheet and into at least some of spaces within the sheet defined by the nanofibers). An adhesive nanofiber tape is formed when the infiltrating polymer is an adhesive and the adhesive infiltrates the nanofiber sheet from a one major surface of the nanofiber sheet. In other described examples, some portions of nanofibers in the sheet have been conformally coated with at least one metal layer.