Galaxies do not have borders. From the inner core to the galactic halos, including the remnants of their hierarchical formation to the extended structure of the intracluster light, low surface brightness observations trace the limits of the intergalactic medium providing strong tests for the Cold Dark Matter standard cosmological model. Pushing the surface brightness limits to such faint levels is extremely hard, requiring an increasing advance in image processing. In this talk we will comment on some of the lessons learned from Low Surface Brightness astronomy with Hubble, and how these will affect the prospects for the Euclid space telescope and other observatories. But more importantly, we will try to answer the question "What is the low surface brightness Universe?"