This review focuses on a now well-established model for generating cells of the trophoblast (TB) lineage by treating human embryonic stem cells (ESC) and induced pluripotent stem cells (iPSC) with the growth factor BMP4. We first discuss the opposing roles of FGF2 and BMP4 in directing TB formation and the need to exclude the former from the growth medium to minimize the co-induction of mesoderm and endoderm. Under these conditions, there is up-regulation of several transcription factors implicated in TB lineage emergence within 3 h of BMP4 exposure and, over a period of days and especially under a high O2 gas atmosphere, gradual appearance of cell types carrying markers for more differentiated TB cell types, including extravillous TB and syncytioTB. We describe the potential value of including low molecular weight pharmaceutical agents that block activin A (INHBA) and FGF2 signaling to support BMP4-directed differentiation. We contend that the weight of available evidence supports the contention that BMP4 converts human ESC and iPSC of the so-called epiblast type unidirectionally to TB. We also consider the argument that BMP4 treatment of human ESC in the absence of exogenous FGF2 leads only to the emergence of mesoderm derivatives to be seriously flawed. Instead, we propose that, when signaling networks supporting pluripotency ESC or iPSC become unsustainable and when specification towards extra-embryonic mesoderm and endoderm are rendered inoperative, TB emerges as a major default state to pluripotency.