Nonlocal continuum models typically take the form of integro-differential equations, replacing the traditional partial differential equations. These models prove effective in various applications, such as the study of fracture and damage using peridynamics and traffic flow using nonlocal traffic models. However, new challenges arise in the numerical simulation of these models with nonlocality involved. In this talk, we offer examples demonstrating our work in theoretical analysis and practical implementation of nonlocal models, which are distinguished by a length parameter defining the effective range of nonlocal interactions. These include developing nonlocal vector calculus and calculus of variations, treating interfaces and boundaries, and ensuring the asymptotic compatibility of numerical schemes under the change of the nonlocal length parameter.
