Decellularization is the process by which cells are discharged from tissues/organs, but all of the essential cues for cell preservation and homeostasis are retained in a three-dimensional structure of the organ and its extracellular matrix components. During tissue decellularization, maintenance of the native ultrastructure and composition of the extracellular matrix (ECM) is extremely acceptable. For recellularization, the scaffold/matrix is seeded with cells, the final goal being to form a practical organ. In this review, we focus on the biological properties of the ECM that remains when a variety of decellularization methods are used, comparing recellularization technologies, including bioreactor expansion for perfusion-based bioartificial organs, and we discuss cell sources. In the future, decellularization-recellularization procedures may solve the problem of organ assembly on demand.