Computer models play an increasingly important role in engineering design and in the study of complex systems, where physical experiments on the real system or even a prototype are prohibitively expensive. Both deterministic and stochastic computer models are used in these situations. A deterministic computer model is a set of complex equations whose solution depends on the input conditions and the levels of design factors or parameters but not on random elements. Examples include finite element models and computational fluid dynamics models. Spacefilling designs are usually employed to study these deterministic computer models and often the modeling strategy involves fitting a spatial correlation or Kriging model (the Gaussian stochastic process model) to the data, because this model interpolates the experimental data exactly.We provide a survey of these designs and the modeling strategy, and propose a new type of hybrid space-filling design. The new design is a hybrid consisting of design points from a traditional space-filling design augmented by runs from a near saturated I-optimal design for a polynomial. We illustrate the construction of these designs with examples, and demonstrate their performance in response prediction for several situations. A comparison with standard space-filling designs is provided.