Organ-on-a-chip has emerged as a powerful platform with widespread applications in biomedical engineering, such as pathology studies and drug screening. However, the fabrication of organ-on-a-chip is still a challenging task due to its complexity. For an integrated organ-on-a-chip, it may contain four key elements, i.e., a microfluidic chip, live cells/microtissues that are cultured in this chip, components for stimulus loading to mature the microtissues, and sensors for results readout. Recently, bioprinting has been used for fabricating organ-on-a-chip as it enables the printing of multiple materials, including biocompatible materials and even live cells in a programmable manner with a high spatial resolution. Besides, all four elements for organ-on-a-chip could be printed in a single continuous procedure on one printer; in other words, the fabrication process is assembly free. In this paper, we discuss the recent advances of organ-on-a-chip fabrication by bioprinting. Light is shed on the printing strategies, materials, and biocompatibility. In addition, some specific bioprinted organs-on-chips are analyzed in detail. Because the bioprinted organ-on-a-chip is still in its early stage, significant efforts are still needed. Thus, the challenges presented together with possible solutions and future trends are also discussed.