Buildings and symmetric spaces both serve as spaces on which algebraic groups act. We will give an overview of both theories and point out some connections. We will take a closer look at a way to construct a non-discrete affine building starting from a model of a symmetric space of non-compact type, suggested by Kramer and Tent in 2003. The construction relies on non-Archimedean real closed fields and uses tools from Lie groups and real algebraic geometry to model theory.