The advent of stem cell based therapies has brought regenerative medicine into an increased focus as a part of the modern medicine practice, with a potential to treat a myriad of intractable diseases in the future. Stem cells reside in a complex microenvironment presenting them with a multitude of potential cues that are chemical, physical, and mechanical in nature. Conventional techniques used for experiments involving stem cells can only poorly mimic the physiological context, and suffer from imprecise spatial and temporal control, low throughput, lack of scalability and reproducibility, and poor representation of the mechanical and physical cell microenvironment. Novel lab-on-a-chip platforms, on the other hand, can much better mimic the complexity of in vivo tissue milieu and provide a greater control of the parameter variation in a high throughput and scalable manner. This capability may be especially important for understanding the biology and cementing the clinical potential of stem cell based therapies. Here we review microfabrication- and microfluidics-based approaches to investigating the complex biology of stem cell responses to changes in the local microenvironment. In particular, we categorize each method based on the types of controlled inputs it can have on stem cells, including soluble biochemical factors, extracellular matrix interactions, homotypic and heterotypic cell-cell signaling, physical cues (e.g. oxygen tension, pH, temperature), and mechanical forces (e.g. shear, topography, rigidity). Finally, we outline the methods to perform large scale observations of stem cell phenotypes and high-throughput screening of cellular responses to a combination of stimuli, and many new emerging technologies that are becoming available specifically for stem cell applications.