A very large number of scientific and engineering fields are confronted with the need for computer simulations to study complex, real world phenomena or solve challenging design problems. However, due to the computational cost of these high fidelity simulations, the use of neural networks, kernel methods, and other surrogate modeling techniques have become indispensable. Surrogate models are compact and cheap to evaluate, and have proven very useful for tasks such as optimization, design space exploration, prototyping, and sensitivity analysis. Consequently, in many fields there is great interest in tools and techniques that facilitate the construction of such regression models, while minimizing the computational cost and maximizing model accuracy. This dissertation presents a mature, flexible, and adaptive framework for regression modeling and adaptive sampling to tackle these issues. The framework brings together algorithms for data fitting, model selection, sample selection, hyperparameter optimalization, and distributed computing in order to empower a domain expert to efficiently generate an accurate model for his/her problem.