Kac-Moody groups form an infinite-dimensional generalization of reductive groups, constructed from infinite root systems. For instance, loop groups of reductive groups are Kac-Moody groups. Whereas their behavior over finite or complex fields is very similar to the reductive setting, many constructions fall apart over p-adic or function fields. In this first talk, I will present a building theoretic approach to this problem and introduce the Kac-Moody analog to affine Weyl groups. Even though these are no longer Coxeter groups, they present combinatorial similarities which I will discuss.