Watched a Ted talk by a Zimbabwean farmer where he talks about how to 'greenify' places that are experiencing desertification.
His method is to basically manage your grazing by assigning your animals into a small area, and as a result they eat all of the plants instead of selectively grazing in a larger area. When the plot has been grazed, they are rotated to another area and so on.
The end results are quite amazing, fairly sustainable too.