Emulating physics-based models is vital for maximizing the science return of next-generation instruments and enabling near-real-time digital twins, rapid discovery, and rigorous uncertainty quantification. This session seeks to showcase an assemblage of specific emulator or surrogate frameworks—whether using reduced-order physics, statistical methods, or machine learning—that are well suited for different modeling challenges such as overcoming computational bottlenecks or improving model understanding and uncertainties. We invite contributions that discuss motivations for emulator and surrogate technology and present architectures tested for specific scientific applications. We encourage sharing lessons learned, particularly regarding interactions across varying spatial, temporal, and spectral scales, adherence to physical laws, and domain-specific validation strategies. By bringing together these techniques, this session aims to map the landscape of advanced computational methods, evaluate transferability between domains, and advance our collective technical literacy of this emergent technology space.