Composite materials are provided that include nanostructures bound together by a binder material in a manner that provides the composite material with high strain capability and toughness. The nanostructures and binder material form a matrix material in which long fiber reinforcements may be embedded to form a structural composite material. The nanostructures may have relatively low aspect ratios, preventing entanglement during processing. The nanostructures can be arranged in an interconnected network to form a high free-volume skeletal structure within the matrix material that allows the nanostructures to flex and return to their original shapes. As applied to ceramic matrix composite (CMC) materials, this tough, flexible matrix material allows for full bonding of the matrix material with the fiber reinforcements so that CMC materials can realize the full potential of the reinforcing fibers and possess superior inter-laminar strength.