Electric aviation and unmanned aerial vehicles (UAVs) depend on lightweight composites to preserve payload and range, yet mass reduction, recycled content, or bio-based content alone does not establish component suitability. Candidate systems must also satisfy coupled structural, thermal, fire, electrical, manufacturing, durability, repair, and circularity requirements. This structured critical narrative review evaluates thermoplastic carbon-fibre-reinforced polymer (CFRP) systems, recycled-carbon-fibre composites, natural-fibre systems, bio-based and recyclable matrices, hybrid architectures, and multifunctional composites using a component-specific framework based on source role, evidence maturity, test comparability, and failure consequence. The framework links processing and chemistry to defects, retained performance, repair and recovery, and the evidence required for defined aircraft and UAV components. Thermoplastic CFRP provides the strongest near-term pathway for secondary and semi-structural components, although weld durability, impact tolerance, fire response, and process conformity remain system specific. Recycled-carbon-fibre and natural-fibre systems are most defensible for lower-consequence covers, fairings, housings, interiors, and UAV parts when feedstock variability, moisture, porosity, and fire performance are controlled. Battery enclosures, primary structures, rotor-support members, and structural-battery systems require representative coupled-hazard and component-scale evidence. The resulting adoption pathways are bounded by component and operating conditions, with manufacturing, durability, repair, recovery, and qualification evidence specified for each application.