The invention relates to methods for culturing human embryonic stem cells by culturing the stem cells in an environment essentially free of mammalian fetal serum and in a stem cell culture medium including amino acids, vitamins, salts, minerals, transferring, insulin, albumin, and a fibroblast growth factor that is supplied from a source other than just a feeder layer the medium. Also disclosed are compositions capable of supporting the culture and proliferation of human embryonic stem cells without the need for feeder cells or for exposure of the medium to feeder cells.