The authors consider the analogue of the Dirichlet problem for second-order elliptic integro-differential equations, and the viscosity solutions approach where the Dirichlet boundary condition may be satisfied only in a generalized sense. They look for conditions on the differential and the integral parts of the equation in order to ensure that the Dirichlet boundary condition is satisfied in the classical sense. They study the behavior of solutions at the boundary in different cases. They start with a linear equation involving the fractional Laplacian on the half-space, and they generalize this to a large class of Lévy operators on smooth domains. They provide an existence result of a continuous viscosity solution to the non-local Dirichlet problem by using Perron’s method.