The goal of tissue engineering is to replace or regenerate damaged tissue. Scaffold fabrications and biomaterial selections are crucial factors for artificial tissue and bone tissue engineering, which are important due to the limited availability of tissue donors. This paper reviews the scaffold design considerations, manufacturing methods, and biomaterials for bone tissue engineering, and discusses current challenges and future perspectives. Scaffolds are required to have non-hazardous properties such as biocompatibility and biodegradability for the human body, and the necessary mechanical properties to support body weight, or to perform other roles, depending on the type of tissue. Moreover, scaffold structures such as porosity, pore size, and pore shape should be optimized to achieve cell viability and proliferation. Many conventional fabrication methods including thermally induced phase separation, emulsion freeze-drying, solvent casting, gas forming, and electrospinning have been studied and developed, but 3D printing is more suitable for bone tissue engineering because of its ability to manufacture complicated structures. Biomaterials can be divided into four categories: polymer, ceramic, metal, and composites. Composites blend two or more biomaterials to achieve desired properties for matching individual patient conditions. Finding a balance between fabrication method and biomaterial selection, in order to match properties between the scaffold and the target tissue, will be key to the field of bone tissue engineering in the future.