The progress as of today of a new class of threshold time series models known as buffered processes is reviewed. In this new class of models switching back and forth between two regimes depends on two different thresholds. We first investigate the self –excited buffered autoregressive (BAR) process to some extent including an identification procedure and the asymptotic properties of the least squares estimators. We then extend the class of models to cover conditional heteroscedasticty resulting in the buffered GARCH and buffered AR-GARCH models.  Simulation studies and applications to real data are considered to illustrate the potential of this new type of threshold models.