Segmental bone defects that are caused by trauma, infection, tumor resection, or osteoporotic fractures present significant surgical treatment challenges. Host bone autograft is considered the gold standard for restoring function but comes with the cost of harvest site comorbidity. Allograft bone is a secondary option but has its own limitations in the incorporation with the host bone as well as its cost. Therefore, developing new bone tissue engineering strategies to treat bone defects is critically needed. In the past three decades, the use of stem cells that are delivered with different scaffolds or growth factors for bone tissue engineering has made tremendous progress. Many varieties of stem cells have been isolated from different tissues for use in bone tissue engineering. This review summarizes the progress in using different postnatal stem cells, including bone marrow mesenchymal stem cells, muscle-derived stem cells, adipose-derived stem cells, dental pulp stem cells/periodontal ligament stem cells, periosteum stem cells, umbilical cord-derived stem cells, peripheral blood stem cells, urine-derived stem cells, stem cells from apical papilla, and induced pluripotent stem cells, for bone tissue engineering and repair. This review also summarizes the progress using exosomes or extracellular vesicles that are delivered with various scaffolds for bone repair. The advantages and disadvantages of each type of stem cell are also discussed and explained in detail. It is hoped that in the future, these preclinical results will translate into new regenerative therapies for bone defect repair.