With the integration and miniaturization of chips, there is an increasing demand for improved heat dissipation. However, the low thermal conductivity (TC) of polymers, which are commonly used in chip packaging, has seriously limited the development of chips. To address this limitation, researchers have recently shown considerable interest in incorporating high-TC fillers into polymers to fabricate thermally conductive composites. Hexagonal boron nitride (h-BN) has emerged as a promising filler candidate due to its high-TC and excellent electrical insulation. This review comprehensively outlines the design strategies for using h-BN as a high-TC filler and covers intrinsic TC and morphology effects, functionalization methods, and the construction of three-dimensional (3D) thermal conduction networks. Additionally, it introduces some experimental TC measurement techniques of composites and theoretical computational simulations for composite design. Finally, the review summarizes some effective strategies and possible challenges for the design of h-BN fillers. This review provides researchers in the field of thermally conductive polymeric composites with a comprehensive understanding of thermal conduction and constructive guidance on h-BN design.