In recent decades, microphysiological constructs and systems (MPCs and MPSs) have undergone significant development, ranging from self-organized organoids to high-throughput organ-on-a-chip platforms. Advances in biomaterials, bioinks, 3D bioprinting, micro/nanofabrication, and sensor technologies have contributed to diverse and innovative biofabrication tactics. MPCs and MPSs, particularly tissue chips relevant to absorption, distribution, metabolism, excretion, and toxicity, have demonstrated potential as precise, efficient, and economical alternatives to animal models for drug discovery and personalized medicine. However, current approaches mainly focus on the in vitro recapitulation of the human anatomical structure and physiological-biochemical indices at a single or a few simple levels. This review highlights the recent remarkable progress in MPC and MPS models and their applications. The challenges that must be addressed to assess the reliability, quantify the techniques, and utilize the fidelity of the models are also discussed.