Oriented thermally conductive phase change composites (PCCs) have attracted significant attention in recent years for their super directional thermal conductivity with a relatively small amount of thermally conductive enhancers (TCEs) and hence less compromise in PCC energy density. Given their unique characteristics and potential applications, this article for the first time provides a comprehensive review of the latest development in the area, covering anisotropic morphologies, heat transfer characteristics, preparation routes, as well as their applicability to their diverse range of potential applications. The review systematically compares the characteristics of oriented thermally conductive PCCs attained through the use of one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) TCEs, respectively. The alignment of highly oriented 1D/2D TCEs is responsible for the enhanced thermal conduction performance, but weak interactions at the interface and the associated thermal resistance are found to be significant barriers that limit the extent of the thermal conductivity enhancement. 3D TCEs are likely to offer continuous conductive networks, as well as PCM shape stabilisation. Based on different characteristics of the TCEs, a relationship is established between anisotropic thermal conductivity of the PCCs and key parameters including concentration, geometry (e.g. dimension, aspect ratio) and the extent of TCE alignment. Additionally, different preparation routes to construct highly oriented thermally conductive networks are reviewed, which can be broadly categorised by applying directional external forces and employing templates with desired structures. Furthermore, potential applications in different fields for the PCCs with directional thermal conduction are summarised. Finally, knowledge gaps and opportunities for further exploration of the oriented thermally conductive PCCs are discussed.