We develop a general distribution-free framework based on conformal prediction for time series, including prediction intervals for real-valued responses and prediction sets for categorical responses. We show that our intervals and sets asymptotically attain valid conditional and marginal coverages for a broad class of prediction functions and time series. We also show that our interval width or set size converges to the oracle prediction interval or set asymptotically. Moreover, we introduce computationally efficient algorithms called \verb|EnbPI| for prediction intervals and \verb|ERAPS| for prediction sets, which wrap up around ensemble predictors. Our framework is closely related to conformal prediction (CP) but does not require data exchangeability. Both algorithms avoid data-splitting and are computationally efficient by avoiding retraining, thus being scalable to sequentially producing prediction intervals or sets. We perform extensive simulation and real-data analyses to demonstrate their effectiveness compared with existing methods. This is a joint work with Chen Xu at Georgia Tech.