###### Abstract
Compost has great value as a soil amendment and fertilizer, with applications in agriculture, horticulture, and gardening, and hence represents a perfect example of a circular economy; in fact, the last decades have seen an increase in compost production. Today, in Europe 42 million tons of waste per annum, that is 59% of the separately collected biowaste, both municipal and commercial/industrial, is composted [20]. An alternative to aerobic composting is vermicomposting. In this case, the transformation and stabilization of organic matter occurs in mesophilic conditions through the combined action of earthworms and microbes. With their movements, the earthworms aerate, mix and grind the substrate, favoring the action of the microbes present in both waste and worms' guts, which are responsible for the biochemical degradation and stabilization of the organic material [21; 22]. Thanks to this synergy, vermicomposting gives a compost with better plant growth promoting properties with respect to aerobic compost, containing a considerable amount of organic acids, such as plant growth hormones and humic acids [23], and higher levels of the most soluble nutrients, such as nitrogen, phosphorus, potassium, calcium and magnesium [24]. Whatever the technology used, knowledge of the transformations of organic matter that take place during the stabilization process, as well as of the composition and quality of the feedstock and of the final product, is fundamental for the agricultural application of the stabilized waste and for the optimization of process parameters, also considering that national and international regulations have established stringent requirements for the application of this product as fertilizer or soil amendment in terms of organic carbon content, humic substance content, etc. For these reasons, since the 1990s, many studies have been published in the scientific literature testing and comparing different chemical and instrumental methods for assessing compost stability and/or maturity, as, for example, measurement of pH, electrical conductivity, CO\({}_{2}\) evolution rate, seed germination rate, dissolved organic carbon, volatile organic carbon, C/N ratio, and humic acid content (seefor instance [25; 26; 27; 28; 29; 30; 31]). To this end, besides conventional analytical methods, advanced instrumental techniques, such as thermal analyses, Fourier transform infrared spectroscopy (FTIR), UV-Vis and fluorescence spectroscopies, nuclear magnetic resonance spectroscopy (NMR), gas chromatography-mass spectrometry, and scanning electron microscopy, can be used to assess the stabilization of organic matter and the quality of the final product. In fact, these techniques provide detailed information on compositional, functional, and behavioral properties of organic materials, even complex ones such as (vermi) compost and digestate. Nevertheless, it is generally agreed that a combination of analyses is advised for a thorough characterization of these materials. Among the techniques that can give access to compositional information of organic matter (OM), NMR, and solid-state NMR (SSNMR) in particular, stands out as a powerful method to access comprehensive qualitative and quantitative structural information not available from other techniques. Compared to liquid-state NMR, which is useful for studying soluble components, especially those with low molecular weight (see Refs. [32; 33] for a comprehensive review), SSNMR has many advantages when applied to OM: (i) it allows bulk samples to be analyzed without pretreatments or the use of solvents, which may introduce artifacts; (ii) it can be used to investigate insoluble OM samples or fractions; (iii) it allows a much higher sample concentration, enhancing signals and saving instrument time; (iv) it is conservative, i.e., it does not consume sample; (vi) it allows the investigation of anisotropic interactions, averaged out in solution NMR by the fast isotropic tumbling of molecules; (v) it allows domains and heterogeneities to be identified within OM structures.