###### Abstract  
Composting, vermicomposting, and anaerobic digestion are three commonly applied processes for the transformation of organic waste into valuable products for soil amendment. The application of compost, vermicompost, and digestate to soil requires specific properties, such as maturity and stability, strongly related to the composition of organic matter. \({}^{13}\)C solid-state Nuclear Magnetic Resonance (SSNMR) has often been applied to follow the transformation of organic matter during waste treatment processes, as well as to assess the quality of the produced amendments and the effectiveness of the treatments. Thanks to the possibility of associating the \({}^{13}\)C chemical shift to different functional groups of biomacromolecules present in the waste feedstocks and in the final products, thorough characterizations of organic matter have been performed exploiting \({}^{13}\)C cross-polarization magic angle spinning experiments, and semiquantitative descriptions of the evolution of the different groups during composting, vermicomposting and anaerobic digestion have been reported. Here, these studies are reviewed with the aim of highlighting the potential of the application of \({}^{13}\)C SSNMR to these complex materials, as well as the critical issues and perspectives. compost; vermicompost; digestate; waste; extracts; maturity; stability; humic substances; humic acids; \({}^{13}\)C CP-MAS +
Footnote †: journal: Applied  
a complex multi-step process [13] in which the organic matter is broken down by different types of anaerobic microorganisms. The first step is the hydrolysis of lipids, proteins and carbohydrates by extracellular enzymes, yielding oligomers and monomers, which are converted to fatty acids and alcohols in the second step. Oxidation of the fatty acids produces acetic acid, H\({}_{2}\) and CO\({}_{2}\), which are transformed to CH\({}_{4}\) by methanogens in the final step. Thus, AD products are biogas (namely, CH\({}_{4}\), CO\({}_{2}\), and, in some cases, H\({}_{2}\)) that are used for renewable energy generation, and a nutrient-rich solid residue, called digestate, which can find application in agriculture, either used directly as a soil amendment or fertilizer or further processed through composing [14; 15; 16]. It should be pointed out that generally digestate requires a short composting period to reach full stability and maturity. Given its ease of implementation and low operational costs, a more commonly used organic waste treatment is composting [17]. Composting is the decomposition process of organic matter performed in aerobic conditions by microorganisms [18], which allows the transformation of organic wastes of different kinds, both vegetal and animal, into a stable organic substance rich in \"humus\". Humans is constituted by the high molecular weight association of amphiphilic compounds, rich in carboxylic groups, slow to decompose under natural conditions, and is responsible for many physicochemical properties that ensure soil fertility. The composting process is naturally driven by microorganisms, which use organic matter and oxygen for their metabolism, producing heat, CO\({}_{2}\), H\({}_{2}\)O, minerals and stable organic matter [19]. This process starts with a bio-oxidative phase characterized by a rising temperature, which reaches 45-70 \({}^{\circ}\)C. During this phase, which lasts for days, thermophilic microorganisms ensure very fast organic matter decomposition, using the most easily available substances. The high temperature ensures sanitation, i.e., the inactivation of most pathogens and invasive plant seeds. Afterwards, the temperature progressively decreases to mesophilic conditions, and the fresh compost enters a curing phase, which can last for weeks, in which decomposition continues, involving the more recalcitrant compounds (such as lignin) and bringing to the formation of humic compounds (fulvic and humic acids, and humin) with high maturity and stability.