Human embryonic stem cells (HESCs) are the in vitro descendants of the pluripotent inner cell mass (ICM) of human blastocyst stage embryos. HESCs can be kept undifferentiated in culture or be differentiated to tissues representing all three germ layers, both in vivo and in vitro. These properties make HESC-based therapy remarkably appealing for the treatment of various disorders. Upon transplantation in vivo, undifferentiated HESCs rapidly generate the formation of large tumors called teratomas. These are benign masses of haphazardly differentiated tissues. Teratomas also appear spontaneously in humans and in mice. When they also encompass a core of malignant undifferentiated cells, these tumors are defined as teratocarcinomas. These malignant undifferentiated cells are termed embryonic carcinoma (EC), and are the malignant counterparts of embryonic stem cells. Here we review the history of experimental teratomas and teratocarcinomas, from spontaneous teratocarcinomas in mice to induced teratomas by HESC transplantation. We then discuss cellular and molecular aspects of the tumorigenicity of HESCs. We also describe the utilization of HESC-induced teratomas for the modeling of early human embryogenesis and for modeling developmental diseases. The problem of HESC-induced teratomas may also impede or prevent future HESC-based therapies. We thus conclude with a survey of approaches to evade HESC-induced tumor formation.