We discuss the utilization of micro-bioreactor arrays for controlling cellular environments in studies of factors that regulate the differentiation of human embryonic stem cells. To this end, we have designed a simple and practical system that couples a microfluidic platform with an array of micro-bioreactors, and has the size of a microscope slide [E. Figallo, C. Cannizzaro, S. Gerecht, J.A. Burdick, R. Langer, N. Elvassore, G. Vunjak-Novakovic, Lab Chip 7 (2007) 710-719]. The system allows quantitative studies of cells cultured in monolayers or encapsulated in three-dimensional hydrogels. We review the operating requirements for studies of human embryonic stem cells (hESCs) under steady-state and dynamic conditions, and the related control of the mass transport and hydrodynamic shear. We describe the design and fabrication of the individual bioreactor components, and the criteria for selecting the bioreactor configuration and operating parameters, based on the analysis of the characteristic times and scales of reaction, convection and diffusion. To illustrate the utility of the bioreactor, we present a "case study" of hESC cultivation with detailed experimental methods and representative biological readouts.