In recent decades metric geometry has become increasingly important and widespread. I will describe certain metric space tools and concepts that are analogous to theorems and notions in functional analysis. Applications to topics in ergodic theory, complex analysis, topology, game theory and deep learning may be mentioned. In particular, even for purely linear problems, metric methods can be useful. The oldest instance might be studies of groups of 2x2 matrices acting instead on the hyperbolic plane. More than that, it turns out that metric notions are in several situations necessary even to formulate a statement that is valid in full generality, almost like a completion of linear spaces with metric notions (on a different level than the usual completion of the rationals by the reals).