The potential for the formation of teratomas or other neoplasms is a major safety roadblock to clinical application of pluripotent stem cell therapies. Preclinical assessment of the risk of tumor formation in this context poses considerable scientific and regulatory challenges, especially because animal xenograft models may not properly reflect the long-term tumorigenic potential of human cells. A better understanding of the biology of spontaneously occurring teratomas and related tumors in humans can help to guide efforts to assess and minimize the potential hazards of embryonic stem cell or induced pluripotent stem cell therapeutics. Here we review the features of teratomas derived experimentally from human pluripotent stem cells and argue that they most closely resemble spontaneous benign teratomas that occur early in both mouse and human life. The natural history and pathology of these spontaneously occurring teratomas provide important clues for preclinical safety assessment and patient monitoring in trials of stem cell therapies.