In this paper we bring together a number of recent studies associated with the burning of low-exothermicity porous materials that are inadvertently, or otherwise, exposed to a maintained heat source (hotspot). Additionally, we provide some new results in the form of dimensionless ignition criteria, which allow us to generalize previous results to a broader class of materials and to larger sample sizes. It is shown that systems of the type described can be represented by a hierarchy of mathematical models, depending on whether oxygen is in limited supply, is not required (as in the case of thermal decomposition), and/or a significant volume of gaseous products is present. We summarize the behaviour of systems in which gas motion through the solid pores has a negligible effect, including cases where the burning is dependent on a limited supply of oxygen. The effects of geometry and initial-boundary conditions are discussed. Finally, for reactions involving gaseous products, we present numerical solutions to a system of equations that incorporates the gas motion through the solid pores by employing Darcy's law. In comparison with the previous cases, it is demonstrated that ignition of low-exothermicity materials is more difficult to achieve (a larger hotspot heat-flux is required), essentially because of transportation of heat by advection towards the unburnt solid, and, consequently, increased reactant depletion. Furthermore, ignition will always take place away from the hot-spot surface; this is in complete contrast to highly exothermic materials, in which reactant depletion is negligible during the early stages of ignition, and in which ignition occurs at the hotspot boundary.