This paper provides review updates on the current development of bionanocomposites with polymeric matrices consisting of synthetic biodegradable aliphatic polyesters reinforced with nanohydroxyaptite (nHA) and/or graphene oxide (GO) nanofillers for bone tissue engineering applications. Biodegradable aliphatic polyesters include poly(lactic acid) (PLA), polycaprolactone (PCL) and copolymers of PLA-PGA (PLGA). Those bionanocomposites have been explored for making 3D porous scaffolds for the repair of bone defects since nHA and GO enhance their bioactivity and biocompatibility by promoting biomineralization, bone cell adhesion, proliferation and differentiation, thus facilitating new bone tissue formation upon implantation. The incorporation of nHA or GO into aliphatic polyester scaffolds also improves their mechanical strength greatly, especially hybrid GO/nHA nanofilllers. Those mechanically strong nanocomposite scaffolds can support and promote cell attachment for tissue growth. Porous scaffolds fabricated from conventional porogen leaching, and thermally induced phase separation have many drawbacks inducing the use of organic solvents, poor control of pore shape and pore interconnectivity, while electrospinning mats exhibit small pores that limit cell infiltration and tissue ingrowth. Recent advancement of 3D additive manufacturing allows the production of aliphatic polyester nanocomposite scaffolds with precisely controlled pore geometries and large pores for the cell attachment, growth, and differentiation in vitro, and the new bone formation in vivo.