Slash and burn agriculture used to be one of the most common ways that we farmed. We would clear a patch of forest and burn the slash to release vital nutrients before planting crops. After a few years when soil fertility declined we would move on and clear another patch of forest and let the original patch regrow back into forest. This was a great system when most farmers did not have access to other sources of plant nutrients like livestock or chemical fertilizes, and when there weren't many farmers. It worked particularity well in the tropics where soils have generally low fertility and where there used to be vast tracts of forest.
Most farmers don't practice slash and burn agriculture nowadays, but a significant few still do--- primarily in regions that also support the last remaining bits of tropical forest. In the best of years slash and burn systems just provide a meager subsistence living to people while contributing to biodiversity loss and environmental degradation.
On potential solution is to give slash and burn farmers the tools to transition into more sustainable practices based on agroforestry. There are a variety of agroforestry systems, this website describes projects based around trees in the genus
Inga.
http://www.ingafoundation.org/the-inga-tree/
The video at the top of the right panel gives a brief overview of their work.