This bachelor's thesis discusses from an ergodic-theoretical perspective the "metric functional analysis" that Anders Karlsson and others have developed in the recent years. We introduce a new symbolic calculus for metric functionals which includes a notion of the adjoint of a nonexpansive map. Using these tools we revisit many central results, including Karlsson's spectral principle and its stronger form for star-shaped spaces due to Gaubert and Vigeral, as well as the multiplicative ergodic theorem of Karlsson-Ledrappier.