Recent advances in integrating microengineering and tissue engineering have generated promising microengineered physiological models for experimental medicine and pharmaceutical research. Here we review the recent development of microengineered physiological systems, or organs on chips, that reconstitute the physiologically critical features of specific human tissues and organs and their interactions. This technology uses microengineering approaches to construct organ-specific microenvironments, reconstituting tissue structures, tissue–tissue interactions and interfaces, and dynamic mechanical and biochemical stimuli found in specific organs, to direct cells to assemble into functional tissues. We first discuss microengineering approaches to reproduce the key elements of physiologically important, dynamic mechanical microenvironments, biochemical microenvironments, and microarchitectures of specific tissues and organs in microfluidic cell culture systems. This is followed by examples of microengineered individual organ models that incorporate the key elements of physiological microenvironments into single microfluidic cell culture systems to reproduce organ-level functions. Finally, microengineered multiple organ systems that simulate multiple organ interactions to better represent human physiology, including human responses to drugs, is covered in this review. This emerging organs-on-chips technology has the potential to become an alternative to 2D and 3D cell culture and animal models for experimental medicine, human disease modeling, drug development, and toxicology.