Anaerobic digestion (AD) is a useful process that could be utilized for food waste (FW) management. Previous studies have shown that carbon materials (CMs) could be an important additive for increasing biomethane yield. However, why CMs improve AD is still uncertain. A significant body of research has been dedicated to investigating the impact of CMs supplementation on biogas production. However, this article specifically emphasizes examining this effect concerning the specific surface area and the functional groups (e.g. hydroxyl groups, carbonyl groups, or unsaturated carbon structures) present on the surface of CMs, produced by torrefaction-TP (240 °C/60 min), pyrolysis-BC (600 °C/60 min), and hydrothermal carbonization-HC (240 °C/60 min/6-10 Bar) processes. The analyses showed that the size of the specific surface area of the CMs (TP-7.72 m g, BC- 115.00 m g, HC-5.46 m g), does not correspond to the production of biomethane. The highest biomethane potential was found for CMs with the lowest SSA, precisely TP and HC, equal to 407 and 394 mL gVS, which was about 13 and 9% higher than production from FW as a sole source of carbon, respectively. The FTIR analysis confirmed the abundance of different organic functional groups on the surface of TP and HC, which could contribute to improved AD performance. These organic residuals, as thermal degradation products, could be an additional source of carbon for microorganisms. The addition of BC, with the highest SSA, decreased the first-order biomethane rate constant k by 16.4% in comparison to food waste without CMs, which could be related to the presence of harmful, more complex organic compounds on the surface of biochar.