Qualification and certification for additive and smart manufacturing systems can be uncertain and very costly. Using available historical data can mitigate some costs of producing and testing sample parts. However, use of such data lacks the flexibility to represent specific new problems which decreases predictive accuracy and efficiency. To address these compelling needs, in this dissertation modeling techniques are introduced that can proactively estimate results expected from additive and smart manufacturing processes swiftly and with practical levels of accuracy and reliability. More specifically, this research addresses the current challenges and limitations posed by use of available data and the high costs of new data by tailoring statistics-based metamodeling techniques to enable affordable prediction of these systems. The result is an integrated approach to customize and build predictive metamodels for the unique features of additive and smart manufacturing systems. This integrated approach is composed of five main parts that cover the broad spectrum of requirements. A domain-driven metamodeling approach uses physics-based knowledge to optimally select the most appropriate metamodeling algorithm without reliance upon statistical data. A maximum predictive error updating method iteratively improves predictability from a given dataset. A grey-box metamodeling approach combines statistics-based black-box and physics-based white-box models to significantly increase predictive accuracy with less expensive data overall. To improve computational efficiency for large datasets, a dynamic metamodeling method modifies the traditional Kriging technique to improve its efficiency and predictability for smart manufacturing systems. Finally, a super-metamodeling method optimizes results regardless of problem conditions by avoiding the challenge with selecting the most appropriate metamodeling algorithm. To realize the benefits of all five approaches, an integrated metamodeling process was developed and implemented into a tool package to systematically select the suitable algorithm, sampling method, and combination of models. All the functions of this tool package were validated and demonstrated by the use of two empirical datasets from additive manufacturing processes.