The article provides state-of-the-art research on agglomeration processes during fixed-bed combustion and gasification of low-grade fuels such as biomass and waste (primarily plastic-containing waste). Such fuels demonstrate complex thermal behaviour: their decomposition and combustion are multistage, accompanied by phase transitions, and may lead to fixed-bed mechanical instability and the non-uniformity of air distribution over the cross-section. To clarify the role of physicochemical factors (fuel composition and properties, reactor conditions), data from different sources are compared. The review shows that the fixed-bed agglomeration regimes can, in a rough approximation, be classified by the sintering mechanism (due to the melting of the mineral part or the organic part), with the following search for each mechanism realisation conditions by comparing the fuel properties and characteristic temperatures. Attempts to theoretically describe and numerically simulate the agglomeration phenomenon as a change in the structure of a reacting dispersed medium are also considered: the main directions in which such approaches can be developed are indicated.