Surrogate models are indispensable in the analysis of engineering systems. The quality of surrogate models is determined by the data quality and the model class but achieving a high standard of them is challenging in complex engineering systems. Heterogeneity, implicit constraints, and extreme events are typical examples of the factors that complicate systems, yet they have been underestimated or disregarded in machine learning. This dissertation is dedicated to tackling the challenges in surrogate modeling of complex engineering systems by developing the following machine learning methodologies. (i) Partitioned active learning partitions the design space according to heterogeneity in response features, thereby exploiting localized models to measure the informativeness of unlabeled data. (ii) For the systems with implicit constraints, failure-averse active learning incorporates constraint outputs to estimate the safe region and avoid undesirable failures in learning the target function. (iii) The multi-output extreme spatial learning enables modeling and simulating extreme events in composite fuselage assembly. The proposed methods were applied to real-world case studies and outperformed benchmark methods. / Doctor of Philosophy / Data-driven decisions are ubiquitous in the engineering domain, in which data-driven models are fundamental. Active learning is a subdomain in machine learning that enables data-efficient modeling, and extreme spatial modeling is suitable for analyzing rare events. Although they are superb techniques for data-driven modeling, existing methods thereof cannot effectively address modern engineering systems complicated by heterogeneity, implicit constraints, and rare events. This dissertation is dedicated to advancing active learning and extreme spatial modeling for complex engineering systems by proposing three methodologies. The first method is partitioned active learning that efficiently learns systems, changing their behaviors, by localizing the information measurement. Second, failure-averse active learning is established to learn systems subject to implicit constraints, which cannot be analytically solved, and to minimize constraint violations. Lastly, the multi-output extreme spatial model is developed to model and simulate rare events that are associated with extremely large values in the aircraft manufacturing system. The proposed methods overcome the limitations of existing methods and outperform benchmark methods in the case studies.