The intestinal tract is a crucial part of the body for growth and development, and its dysregulation can cause several diseases. The lack of appropriate in vitro models hampers the development of effective preventions and treatments against these intestinal tract diseases. Intestinal organoids are three-dimensional (3D) polarized structures composed of different types of cells capable of self-organization and self-renewal, resembling their organ of origin in architecture and function. Porcine intestinal organoids (PIOs) have been cultured and are used widely in agricultural, veterinary, and biomedical research. Based on the similarity of the genomic sequence, anatomic morphology, and drug metabolism with humans and the difficulty in obtaining healthy human tissue, PIOs are also considered ideal models relative to rodents. In this review, we summarize the current knowledge on PIOs, emphasizing their culturing, establishment and development, and applications in the study of host–microbe interactions, nutritional development, drug discovery, and gene editing potential.