Several methods for creating vascular structures, made of either discrete or interconnected channels have been developed. The currently employed methods enable the formation of channels with diameters in the millimetric and micrometric scale. However, the formation of an interconnected three-dimensional (3D) vasculature by using a rapid and scalable process is a challenge and largely limits the fields of applicability of these innovative materials. Here, we propose the use of electrospun nonwoven mats as sacrificial fibers to easily generate 3D macroscale vascularized composites containing interconnected networks with channels and tubes having submicrometric and nanometric diameters. The novel approach has the potentialities to give rise to a novel generation of composites potentially displaying new and enhanced functionalities thanks to the nanoscale features of the cavities.