We study the space of maximal flats of symmetric spaces of non-compact type or of Euclidean buildings: we define a geometric compactification by looking at the visual limits of a diverging sequence of flats. We completely determine the possible degenerations of flats when X is of rank 1, associated to a classical group of rank 2 or to PGL(4). In particular, we exhibit unexpected behaviours of visual limits of maximal flats in various symmetric spaces of small rank and surprising algebraic restrictions that occur.