We describe in this chapter the development of a xenofree molecularly defined medium, SBX, associated with xenofree matrices, to maintain human embryonic stem cell (hESC) pluripotency as determined by phenotypic, functional and TLDA studies. This simple, inexpensive, and more physiological culture condition has been chosen because (1) it is xenofree and molecularly defined; it is devoid of albumin, which is a carrier of undefined molecules; (2) it maintains pluripotency, but very significantly reduces differentiation gene expression during hESC self-renewal, as compared to the widely used culture conditions tested so far; and (3) it can be further improved by replacing high concentrations of expensive additives by physiological concentrations of new factors. Xenofree molecularly defined media and matrices represent valuable tools for elucidating still unknown functions of numerous embryonic genes using more physiological culture conditions. These genes encode potential new factors controlling hESC self-renewal and pluripotency.