Drug discovery and development to date has relied on animal models, which are useful but are often expensive, slow, and fail to mimic human physiology. The discovery of human induced pluripotent stem (iPS) cells has led to the emergence of a new paradigm of drug screening using human and disease-specific organ-like cultures in a dish. Although classical static culture systems are useful for initial screening and toxicity testing, they lack the organization of differentiated iPS cells into microphysiological, organ-like structures deemed necessary for high-content analysis of candidate drugs. One promising approach to produce these organ-like structures is the use of advanced microfluidic systems, which can simulate tissue structure and function at a micron level, and can provide high-throughput testing of different compounds for therapeutic and diagnostic applications. Here, we provide a brief outline on the different approaches, which have been used to engineer in vitro tissue constructs of iPS cell-based myocardium and liver functions on chip. Combining these techniques with iPS cell biology has the potential of reducing the dependence on animal studies for drug toxicity and efficacy screening.