Linear processes with long range dependence are obtained by linear filtering of white noise using a fractional integration operator. Integrated on large scales, such processes can be approximated by a fractional Brownian motion. In the non-linear case, with similar second-order properties, such an approximation no longer holds. We will recall different limit distributions that may appear in the large scale asymptotic, depending on the type of non-linearity. The goal of this talk is to present recent results applying to non-linear long range dependent processes that go beyond the large scale approximation. For instance, we will answer the following question: is the large scale approximation sufficient to determine the asymptotic behavior of standard estimators of the long memory parameter ?