This review is focused on hybrid polyhydroxyalkanoate-based (PHA) biomaterials with improved physico-mechanical, chemical, and piezoelectric properties and controlled biodegradation rate for applications in bone, cartilage, nerve and skin tissue engineering. PHAs are polyesters produced by a wide range of bacteria under unbalanced growth conditions. They are biodegradable, biocompatible, and piezoelectric polymers, which make them very attractive biomaterials for various biomedical applications. As naturally derived materials, PHAs have been used for multiple cell and tissue engineering applications; however, their widespread biomedical applications are limited due to their lack of toughness, elasticity, hydrophilicity and bioactivity. The chemical structure of PHAs allows them to combine with other polymers or inorganic materials to form hybrid composites with improved structural and functional properties. Their type (films, fibers, and 3D printed scaffolds) and properties can be tailored with fabrication methods and materials used as fillers. Here, we are aiming to fill in a gap in literature, revealing an up-to-date overview of ongoing research strategies that make use of PHAs as versatile and prospective biomaterials. In this work, a systematic and detailed review of works investigating PHA-based hybrid materials with tailored properties and performance for use in tissue engineering applications is carried out. A literature survey revealed that PHA-based composites have better performance for use in tissue regeneration applications than pure PHA.