Despite the large use of granular materials in the industry, and the large number of natural phenomena where granular materials are involved, a comprehensive theoretical framework of their physics is still missing. An important perspective was proposed almost 20 years ago by S.Edwards, which suggested the possibility of a statistical mechanics description of granular materials at rest in their mechanically stable states. This article focuses on the theoretical foundations and current understanding of a statistical mechanics approach of granular materials under gravity. Experimental and numerical results discussing such an approach and clarifying its limit of validity are described as well.