Abstract: The term Nonlinear Filtering refers to the problem of reconstructing the state of a nonlinear system (or more generally a Markov Process) from noise corrupted observations in a causal fashion, that is, only past and present measurements are to be taken into account. Nonlinear Filtering appears in scientific fields as different as signal processing, control theory, econometrics, and environmental forecasting, sometimes in different guises and under different names. In this talk, the notion of nonlinear filtering will be motivated and explained. Several illustrative examples are presented. An interesting problem in filtering is the existence of asymptotically stationary filtering processes, which is both mathematically interesting and of relevance in practical applications. Several special cases have been studied, which, although differing in the details, share a common approach. This approach employs the projective Birkhoff metric on suitable cones. The talk will sketch the main ideas behind this approach.