Polydimethylsiloxane (PDMS) is the predominant material used for organ-on-a-chip devices and microphysiological systems (MPSs) due to its ease-of-use, elasticity, optical transparency, and inexpensive microfabrication. However, the absorption of small hydrophobic molecules by PDMS and the limited capacity for high-throughput manufacturing of PDMS-laden devices severely limit the application of these systems in personalized medicine, drug discovery, in vitro pharmacokinetic/pharmacodynamic (PK/PD) modeling, and the investigation of cellular responses to drugs. Consequently, the relatively young field of organ-on-a-chip devices and MPSs is gradually beginning to make the transition to alternative, nonabsorptive materials for these crucial applications. This review examines some of the first steps that have been made in the development of organ-on-a-chip devices and MPSs composed of such alternative materials, including elastomers, hydrogels, thermoplastic polymers, and inorganic materials. It also provides an outlook on where PDMS-alternative devices are trending and the obstacles that must be overcome in the development of versatile devices based on alternative materials to PDMS.