The paper considers the computer model calibration problem and provides a general frequentist solution. Under the framework proposed, the data model is semiparametric with a non-parametric discrepancy function which accounts for any discrepancy between physical reality and the computer model. In an attempt to solve a fundamentally important (but often ignored) identifiability issue between the computer model parameters and the discrepancy function, the paper proposes a new and identifiable parameterization of the calibration problem. It also develops a two-step procedure for estimating all the relevant quantities under the new parameterization. This estimation procedure is shown to enjoy excellent rates of convergence and can be straightforwardly implemented with existing software. For uncertainty quantification, bootstrapping is adopted to construct confidence regions for the quantities of interest. The practical performance of the methodology is illustrated through simulation examples and an application to a computational fluid dynamics model.