The comprehensive description of the thermal degradation and combustion of biomass materials is a very challenging problem, as its complexity occurs at several levels: (1) multi-component problem, with an intrinsic variability of biomass composition; (2) multi-phase problem since the biomass reacts both in the condensed and in the gas phase resulting in the formation of a solid bio-char, a liquid bio-oil, and a gas phase; (3) multi-scale problem since the intra and inter-phase transport phenomena need to be considered both at the particle and reactor scale; and (4) multi-dimensional problem since the overall system could evolve along several coordinates such as the particle radius, biomass bed, and Lime. This complexity is further enhanced by the need of a coupled and comprehensive approach of the transport phenomena and the detailed kinetic schemes both in the solid and gas phase. After a review of the multi-step kinetic model adopted for the pyrolysis of biomass particles, the homogeneous gas phase reactions, and the heterogeneous reactions of the residual char, this paper analyzes the mathematical model at the particle and reactor scale. The mathematical models of a biomass gasifier and a traveling grate combustor constitute two working examples of the different scales from the biomass particle up to whole industrial devices. (C) 2013 Elsevier Ltd. All rights reserved