In this chapter, we give an overview of research related to self-organizing machines that was inspired by biological self-organization. There were various motivations for this kind of research. Von Neumann's work, which we discuss first, was motivated by the purely mathematical question of whether self-reproduction is logically possible or not. Next, we discuss the work by Penrose, who considered the above as a question of actual objects, to be solved with experiments. We then go on to consider some of the studies that followed upon these two. A basso continuo underlying all these studies is a desire to understand the mechanisms behind the biological organisms discussed in the previous chapter. In order to understand these mechanisms, instead of studying biological organisms directly, they focused on some aspects of biological organisms of interest and modeled them. This is called a constructive approach 1. If biological organisms can be understood through a constructive approach, machines can be built according to the derived model.