The present disclosure provides methods for maintaining and propagating undifferentiated pluripotent stem cells (SC) in suspension. The methods comprise culturing such SC in a non-adherent culture dish under conditions comprising a basic serum free medium and one or more of a basic medium, a serum replacement, an extra cellular matrix component and a factor supporting expansion of said SC. A specific and preferred culture condition comprise supplementing Neurobasal™ medium with KO serum replacement (KOSR). These conditions allowed for large scale and long term propagation of undifferentiated pluripotent SC. The culture system comprising suspended undifferentiated pluripotent SC were found to have many applications including in methods for directed as well as spontaneous differentiation of the SC into somatic cells. Also disclosed herein is a method of deriving SC, preferably human embryonic SC from human embryos via the formation of cell clusters.