Anaerobic digestion of organic wastes is clearly encouraged by current regulations in Europe. In complement to the energy supply it represents, this biological treatment process also allows the recycling of organic matter and nutrients contained in biodegradable wastes. Indeed the digestion residue can be further promoted as soil improver or fertilizer. The sustainability of anaerobic digestion plants partly depends on the management of these digestion residues. Digestates present particular characteristics that can reduce their direct agricultural valorization and minimize by the way the benefit of such a biological treatment. Thus the first part of this two part paper aims at reviewing and discussing a wide range of biochemical, biological and physical indicators used to assess the agronomic quality of organic products and the feasibility of an aerobic treatment by composting. The definition of agronomic quality is very complex and no single parameter can be picked out to assess the quality of solid digestates coming from different sources. A relevant choice of these parameters will lead to state on digestates agricultural use, whether they can be directly used on soil after digestion or if they need a composting post-treatment before utilization. The second part of this two part paper will choose indicators to characterize several digestates in order to assess their future agricultural use.