This study provides a concise overview of the latest developments in multifunctional thermally conductive polymer composites (TCPCs). Drawing from the current state of research, the study elucidates the mechanisms that underpin thermal conductivity in polymers and their composites. It further delineates the structure-property relationships of TCPCs, focusing on their modulus, resilience, and orientation. Concurrently, this work delves into the principles and structural design of TCPCs endowed with self-healing capabilities, electromagnetic interference (EMI) shielding, and electrical insulation characteristics. In particular, it outlines design strategies for imparting self-healing features to TCPCs and explores the interplay between thermal conductivity and self-healing efficacy. The principles of EMI shielding are clarified, along with the primary structural variants of TCPCs possessing EMI shielding attributes. Additionally, the paper addresses the insulative treatments applied to fillers within composites to enhance their electrical insulation. It concludes with a brief exposition of applications spanning electronic packaging, batteries, aerospace, LEDs, and flexible&stretchable electronics, to sensors. The aim of this review is to provide fresh insights for researchers intent on devising TCPCs with integrated self-healing, electromagnetic shielding, and electrical insulation functionalities, and to articulate strategies for optimizing the thermal conductivity coefficient (λ) alongside these attributes.