Biodegradable polymers and bioactive ceramics are being combined in a variety of composite materials for tissue engineering scaffolds. Materials and fabrication routes for three-dimensional (3D) scaffolds with interconnected high porosities suitable for bone tissue engineering are reviewed. Different polymer and ceramic compositions applied and their impact on biodegradability and bioactivity of the scaffolds are discussed, including in vitro and in vivo assessments. The mechanical properties of today's available porous scaffolds are analyzed in detail, revealing insufficient elastic stiffness and compressive strength compared to human bone. Further challenges in scaffold fabrication for tissue engineering such as biomolecules incorporation, surface functionalization and 3D scaffold characterization are discussed, giving possible solution strategies. Stem cell incorporation into scaffolds as a future trend is addressed shortly, highlighting the immense potential for creating next-generation synthetic/living composite biomaterials that feature high adaptiveness to the biological environment.