Explore a comprehensive lecture on coupling strategies for nonlocal and local models, focusing on applications in nonlocal elasticity. Delve into the increasing use of nonlocal models in science and engineering, their advantages in capturing complex effects, and the computational challenges they present. Learn about an optimization-based method for coupling nonlocal and local problems, including its formulation, well-posedness, and implementation using Sandia's agile software components toolkit. Examine numerical results for nonlocal diffusion in three dimensions and discover applications in coupling static peridynamics with classical elasticity. Cover topics such as nonlocal vector calculus, model problems, solution uniqueness, coupling error, convergence analysis, and various numerical tests including crack simulations and tensile bar experiments.