The intricate microarchitecture of tissues – the “tissue microenvironment” – is a strong determinant of tissue function. Microfluidics offers an invaluable tool to precisely stimulate, manipulate, and analyze the tissue microenvironment in live tissues and engineer mass transport around and into small tissue volumes. Such control is critical in clinical studies, especially where tissue samples are scarce, in analytical sensors, where testing smaller amounts of analytes results in faster, more portable sensors, and in biological experiments, where accurate control of the cellular microenvironment is needed. Microfluidics also provides inexpensive multiplexing strategies to address the pressing need to test large quantities of drugs and reagents on a single biopsy specimen, increasing testing accuracy, relevance, and speed while reducing overall diagnostic cost. Here, we review the use of microfluidics to study the physiology and pathophysiology of intact live tissues at sub-millimeter scales. We categorize uses as either in vitro studies – where a piece of an organism must be excised and introduced into the microfluidic device – or in vivo studies – where whole organisms are small enough to be introduced into microchannels or where a microfluidic device is interfaced with a live tissue surface (e.g. the skin or inside an internal organ or tumor) that forms part of an animal larger than the device. These microfluidic systems promise to deliver functional measurements obtained directly on intact tissue – such as the response of tissue to drugs or the analysis of tissue secretions – that cannot be obtained otherwise.