There has been great interest in researching and implementing effective technologies for the capture, processing, and display of 3D images. This broad interest is evidenced by widespread international research and activities on 3D technologies. There is a large number of journal and conference papers on 3D systems, as well as research and development efforts in government, industry, and academia on this topic for broad applications including entertainment, manufacturing, security and defense, and biomedical applications. Among these technologies, integral imaging is a promising approach for its ability to work with polychromatic scenes and under incoherent or ambient light for scenarios from macroscales to microscales. Integral imaging systems and their variations, also known as plenoptics or light-field systems, are applicable in many fields, and they have been reported in many applications, such as entertainment (TV, video, movies), industrial inspection, security and defense, and biomedical imaging and displays. This tutorial is addressed to the students and researchers in different disciplines who are interested to learn about integral imaging and light-field systems and who may or may not have a strong background in optics. Our aim is to provide the readers with a tutorial that teaches fundamental principles as well as more advanced concepts to understand, analyze, and implement integral imaging and light-field-type capture and display systems. The tutorial is organized to begin with reviewing the fundamentals of imaging, and then it progresses to more advanced topics in 3D imaging and displays. More specifically, this tutorial begins by covering the fundamentals of geometrical optics and wave optics tools for understanding and analyzing optical imaging systems. Then, we proceed to use these tools to describe integral imaging, light-field, or plenoptics systems, the methods for implementing the 3D capture procedures and monitors, their properties, resolution, field of view, performance, and metrics to assess them. We have illustrated with simple laboratory setups and experiments the principles of integral imaging capture and display systems. Also, we have discussed 3D biomedical applications, such as integral microscopy.