Field-effect transistors based on solution-processible organic semiconductors have experienced impressive improvements in both performance and reliability in recent years, and printing-based manufacturing processes for integrated transistor circuits are being developed to realize low-cost, large-area electronic products on flexible substrates. This article reviews the materials, charge-transport, and device physics of solution-processed organic field-effect transistors, focusing in particular on the physics of the active semiconductor/dielectric interface. Issues such as the relationship between microstructure and charge transport, the critical role of the gate dielectric, the influence of polaronic relaxation and disorder effects on charge transport, charge-injection mechanisms, and the current understanding of mechanisms for charge trapping are reviewed. Many interesting questions on how the molecular and electronic structures and the presence of defects at organic/organic heterointerfaces influence the device performance and stability remain to be explored.