This article discusses the so-called planetary civilization, the origin of which dates back to early modern times and which evolved along with the development of communication systems and the integration of continents by the merchandising exchanges, bringing with it a profound cultural miscegenation throughout the planet. One of the biggest challenges of school education today is, without doubt, educating in and for an era with planetary characteristics in order to awaken a world-society. The consciousness of the existence of a planetary civilization and the ability to live in a common Homeland-Earth, however, depend crucially on a paradigmatic reform of the structure of thought. This new cognitive matrix relies on transdisciplinary principles of complexity theory to understand the reality of biocultural phenomena with planetary features. The concepts of planetary era, world-society, Homeland-Earth, terrestrial citizenship and the planetary man constitute the horizon of meaning of complexity theory. Finally, learning to live in and for a planetary era requires that we civilize thought and live a pragmatic of complexity.