One of the most promising substrate materials for the next-generation power devices with high thermal conductivity is silicon nitride (Si3N4). There are several ways to improve thermal conductivity of Si3N4. Substantially higher thermal conductivities for the Si3N4 ceramics could be attained by reduction of lattice oxygen content or by the increasing the β/α phase ratio during nitridation thus enhancing grain growth during post-sintering. The method of purification of the grains and decreasing the two-grain junction films by adding large β-Si3N4 grains to the raw Si3N4 powder, seeding by grain growth of Si3N4 crystals in polycrystalline ceramics also improves thermal conductivity. High thermal conductivity can be further achieved by development a textured microstructure in which elongated β-Si3N4 grains are oriented almost unidirectionally. This paper summarizes the extrinsic factors governing the thermal conductivity of Si3N4 ceramic regarding microstructural parameters such as lattice defects in single-crystal, sintering additives, change in microstructural parameters like α/β ratio, grain size, aspect ratio, grain orientation and the morphology, composition of grain-boundary, secondary phases, processing method.