Contrasted with the standard linear ARMA models, financial time series exhibits non-standard features such as fat-tails, non-normality, volatility clustering and asymmetries which are usually referred to as "stylized facts" in financial time series context (Terasvirta, 2009). We are accordingly led to ad hoc models (apart from ARMA) to accommodate stylized facts . The paper aims to give a contemporary overview on financial and special time series models based on the recent literature and on the

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... author's publications. Various models are illustrated including asymmetric models, integer valued models, multivariate models and high frequency models. Selected statistical issues on the models are discussed, bringing some perspectives to the future works in this area.