Recent advances on human pluripotent stem cells (hPSCs), including human embryonic stem cells (hESCs) and induced pluripotent stem cells (hiPSCs) have brought us closer to the realization of their clinical potential. Nonetheless, tissue engineering and regenerative medicine applications will require the generation of hPSC products well beyond the laboratory scale. This also mandates the production of hPSC therapeutics in fully-defined, xeno-free systems and in a reproducible manner. Toward this goal, we summarize current developments in defined media free of animal-derived components for hPSC culture. Bioinspired and synthetic extracellular matrices for the attachment, growth and differentiation of hPSCs are also reviewed. Given that most progress in xeno-free medium and substrate development has been demonstrated in two-dimensional rather than three dimensional culture systems, translation from the former to the latter poses unique difficulties. These challenges are discussed in the context of cultivation platforms of hPSCs as aggregates, on microcarriers or after encapsulation in biocompatible scaffolds.