Tissue chips (TCs), otherwise known as organs-on-a-chip (OoC), organ chips (OCs), or microphysiological systems (MPS), are rapidly gaining prominence as an extension of or even replacement for traditional animal models of disease physiology. They also have recognized utility in the context of drug development: for example, data from TCs can now be submitted in place of some animal testing to the FDA. In principle, TCs are structured to allow measurement of any number of outputs that yield information about the tissue. However, to date, measurements made during experiments with TCs have been largely restricted to immunofluorescence microscopy and benchtop assays performed on media extracted from the cell culture within the device. With the development of biosensors that are sensitive and have an ever-shrinking footprint, on-board biosensing is now in the early stages of exploration. This review discusses the importance of tissue chips and the advances in sensing that will aid the complexity and utility of tissue chip research moving forward. We cover several sensing modalities, including electrical and optical sensing modes. Finally, challenges and opportunities for the future are discussed.