Computer models play a key role in many scientific and engineering problems. One major source of uncertainty in computer model experiment is input parameter uncertainty. Computer model calibration is a formal statistical procedure to infer input parameters by combining information from model runs and observational data. The existing standard calibration framework suffers from inferential issues when the model output and observational data are high-dimensional dependent data such as large time series or spatial data due to the difficulty in building an emulator and the non-identifiability between effects from input parameters and data-model discrepancy. In this talk a series of methods that I have been working on to solve these issues will be discussed, including a reduced-dimension approach, a generalized linear model-based framework, a mixture model-based framework, and an inverse model-based approach using deep neural network. The scientific problems that can be solved by these methods will be discussed as well, including generating future projections for the West Antarctic Ice sheet and improving flood forecast in the WRF-hydro model.