Can we 'see' photons, black holes, curved spacetime, quantum jumps, the expansion of the universe, or quanta of space? Physics challenges appearances, showing convincingly that our everyday vision of reality is limited, approximate and badly incomplete. Established theories such as quantum theory and general relativity and investigations like loop quantum gravity have a reputation of obscurity. Many suggest that science is forcing us into a counterintuitive and purely mathematical understanding of reality. I disagree. I think that there is a visionary core at the root of the best science. Where 'visionary' truly means formed by visual images. Our mind, even when dealing with abstract and difficult notions, relies on images, metaphors and, ultimately, vision. Contrary to what is sometimes claimed, science is not just about making predictions: it is about understanding, and, for this, developing new eyes to see. I shall illustrate this point with some concrete cases, including the birth of quantum theory in Einstein’s intuition, curved spacetimes and quanta of space.