The new composite materials have a lot of appeal due to their maintenance-free characteristics, and I highly recommend them, if they go with your architecture and your taste. However for some applications there is nothing like real wood. In fact, most composite decking materials are not structural and can not be used for the posts, beams or floor joists as they are not as rigid as real wood.
Overhead patio structures are usually made of Douglas Fir for a primed and painted look, which may check (crack along the grain) or bleed (moisture or sap) after the first hot summer and may need to be filled and re-painted after the first year.
Redwood decks need bi-yearly attention, which may involve stripping the sealer, water-blasting, acid washing, or sanding and then re-sealing in order to maintain the warm look and to keep it protected. Ipe hardwood decks do not actually need to be treated, as the wood is so dense, left natural they can last for a long time. If you do treat them they need the same yearly or bi-yearly attention to keep the looking their best. For more details, see: deck refinishing