This talk gives an overview of the different approaches used to explore implications of the smallest space-time structures on the largest cosmological scales. Many ideas can be introduced by analogies with systems of condensed-matter physics, with space-time taking the place of atoms. These analogies not only help to understand space-time effects but also enable a transfer of methods and expertise. In contrast to condensed-matter physics, there are no experiments yet that can guide the construction of fundamental space-time theories. But theories are getting closer to being falsifiable by cosmological and astrophysical observations, examples of which will also be discussed
