Biological systems make use of hair and capillary type hierarchical structures to create more surface area in limited space, but very few synthetic materials use this concept. Geometrical calculations show that if hierarchical substrates are created by nanotube grafting on materials having open interconnected porosity, the surface area available for functionalization can increase by three orders of magnitude, without any increase in volume. Until recently, growing nanotube arrays/forests on porous and microcellular surface geometries was extremely difficult. This group has recently achieved that by pre-coating microcellular carbon surface with a plasma-derived nano-oxide layer. The nano-layer enhances catalytic activity and allows subsequent attachment of multi-walled carbon nanotubes (CNT) by CVD. Factors influencing growth of the CNT layer and their properties will be discussed. The helicity of nanotubes can be partly controlled by gas composition, which is a plus since thermal and electronic properties depend upon helicity. A variety of properties influenced by these structures will be presented, such as, but not limited to: (a) Fracture behavior of composites made from CNT grafted porous materials, (b) Influence of CNT grafting on thermal transport, and (c) Enhancement of biological activity and control of cell growth directions with nanotube growth on porous scaffolds.