This talk focuses on statistical inference when the dimension and sample size of multiple time series go to infinity. The serial dependence of the data can affect the asymptotic properties of commonly used statistics and leads to erroneous inference. We use simple examples to demonstrate the impact of serial dependence and increase in dimension on estimating autoregressive models, on eigenanalysis of covariance matrix, and canonical correlation analysis of functions of high-dimensional time series. We then investigate proper adjustments needed to derive the limiting distributions for statistics of interest. Simulation is used to examine the finite sample performance of the statistics and real examples are used to show the applications of high-dimensional time series. This talk is based on joint research with several co-authors, including Yuefeng Han and W.B. Wu (University of Chicago), S. Ling (HKST), and R. Chen (Rutgers).