Abstract: Currently, energy demand and consumption problems have become a focus issue due to rapid economic growth, environmental pollution, and energy shortages. Hence, new technologies must be explored and developed for the recovery of wasted energy or to harness solar energy. Thermal energy storage will not only improve energy utilization efficiency and store wasted heat; it will also ease the problem of energy supply and demand. Thermal energy storage is considered to be one of the most efficient approaches for the sustainable control and utilization of energy. Organic phase-change energy storage as a strategy for thermal energy storage has attracted widespread attention in recent years by virtues of its high latent storage capacity, suitable phase-change temperature, chemical and thermal stability, non-toxicity, and nearly absent supercooling properties. However, the leakage problem and low conductivity of organic phase-change materials during the phase-change process hinder their practical application. Leakage can cause serious environmental damage and reduce thermal energy storage. Low thermal conductivity can result in a large temperature gradient and insensitivity to temperature changes, thereby reducing the heat transfer efficiency of phase-change materials. To solve the above issues, various encapsulation techniques have been developed and substances with high thermal conductivity have become a research hotspot. In this work, we summarized three main approaches—porous absorption, microencapsulation, and electrospinning—to prepare shape-stabilized phase-change materials. For porous absorption, we identified some widely available, low-cost renewable materials that can be used as support material for fabricating composite phase-change materials, such as biomass-derived wood, winter melon, potatoes, and cotton. In addition, the energy conversion mechanism of composite phase-change materials was discussed. The applications of phase-change materials in solar absorption refrigeration systems, solar energy systems, energy storage systems for buildings, passive thermal management of batteries, cold storage, and photovoltaic electricity generation were summarized. Lastly, future research directions on composite phase-change energy storage materials were also proposed.