This paper presents its author’s famous distinction between globalization, as the process or vehicle by which ideas, habits and worldviews travel from one culture to another and are transformed in the process, and mundialization, as the taking in of the outside world into our own lifeworlds, a process by which the ideas and customs of other cultures are transported into our homeworlds. In this process, what was once strange and unfamiliar is transformed into something comfortable and familiar. This is the process that is generally known as cultural assimilation, and by virtue of which the boundaries of our individual homeworlds become constantly widened. Examining this phenomenon, which he calls the ‘mundialization of home’, leads the author to sketch the main features of a possible transcultural moral world.