Dynamic computer experiments are those with time series outputs. Research on such experiments has been gaining momentum recently. In this talk, we consider two problems of dynamic computer experiments. We propose a computationally efficient modeling approach to build emulators for large-scale dynamic computer experiments. This approach sequentially finds a set of local design points based on a new criterion specifically designed for emulating dynamic computer simulators. Singular value decomposition based Gaussian process models are built with the sequentially chosen local data. To update the models efficiently, an empirical Bayesian approach is introduced. When a target observation is available, estimating the inputs of the computer simulator that produce the matching response as close as possible is known as inverse problem. We propose a new criterion-based estimation method to address the inverse problem of dynamic computer experiments.