Most of the recent work in time series analysis has been done on the assumption that the structure of the series can be described by linear models such as Autoregressive (AR), Moving Average (MA) or mixed Autoregressive-Moving Average (ARMA) models. However, there are occasions on which subject matter, theory •or data suggests that linear models are unsatisfactory and hence it is desirable to look at non-linear time series models. In the last decade several non-linear time series models have appeared in literature, specifically, bilinear time series models, threshold AR models, exponential AR models, random coefficient AR models, exponential moving average models and other related models. In this paper we have reviewed various non-linear time series models. We have also reviewed - various tests of non-linearities developed by various authors. Since the model specification is the most important step in any time series model building, we have discussed the problem of model specification in the context of bilinear and threshold models in detail.