Nature leaves no waste, only people do. Nature's waste is sustainable because its decomposition follows a sustainable cycle in which every part feeds the next step in the cycle endlessly. Animal waste and dead plant material compost back into the soil, carrion eating birds and little critters take care of animal carcasses, trees absorb the carbon dioxide that animals and humans exhale. It is only us humans who have devised production processes that transform natural materials into stuff that is either itself not recyclable (think plastics) and creates trash that way, or whose manufacturing produces side effects in the form of waste and pollution (any industrial process).
Worldwide many towns and cities strive to become zero-waste by 2020. The goal of zero-waste is to recycle and compost everything so nothing goes into the landfill. It takes a strong commitment from the city and a persistent education effort to overcome people's initial resistance and learning curve - take a look at this video of a Japanese town that's almost there. Then take a look at your household trash and recycling logistics. Can you do better? You may also want to re-read an older post - trash-free? Since Nature leaves no waste let's remember that we, actually, are Nature, too.