Hydroxyapatite (HAp) polymer composites have gained significant attention due to their applications in bone regeneration and tooth implants. This review examines the synthesis, properties, and applications of Hap, highlighting various manufacturing methods, including wet, dry, hydrothermal, and sol–gel processes. The properties of HAp are influenced by precursor materials and are commonly obtained from natural calcium-rich sources like eggshells, seashells, and fish scales. Composite materials, such as cellulose–hydroxyapatite and gelatin–hydroxyapatite, exhibit promising strength and biocompatibility for bone and tissue replacement. Metallic implants and scaffolds enhance stability, including well-known titanium-based and stainless steel-based implants and ceramic body implants. Biopolymers, like chitosan and alginate, combined with Hap, offer chemical stability and strength for tissue engineering. Collagen, fibrin, and gelatin play crucial roles in mimicking natural bone composition. Various synthesis methods like sol–gel, hydrothermal, and solution casting produce HAp crystals, with potential applications in bone repair and regeneration. Additionally, the use of biowaste materials, like eggshells and snails or seashells, not only supports sustainable HAp production but also reduces environmental impact. This review emphasizes the significance of understanding the properties of calcium–phosphate (Ca-P) compounds and processing methods for scaffold generation, highlighting novel characteristics and mechanisms of biomaterials in bone healing. Comparative studies of these methods in specific applications underscore the versatility and potential of HAp composites in biomedical engineering. Overall, HAp composites offer promising solutions for improving patient outcomes in bone replacement and tissue engineering and advancing medical practices.