In almost all areas of the natural sciences, there arises a need to solve integro-differential equations of the Volterra type. For this purpose, it is proposed here to use multistep, multi-derivative methods with constant coefficients. Several concrete methods are constructed, and it is shown how they can be applied to solve the initial-value problem for Volterra integro-differential equations. It is also shown how the relationship between the solutions of the initial-value problems for both ordinary differential equations and Volterra integro-differential equations can be utilized. For the construction of more accurate numerical methods, it is proposed here to use certain special cases of the multistep, multi-derivative methods. For the comparison of these methods, the concepts of stability and the order of numerical methods are usually used. By using the maximum attainable order for stable methods, optimal methods have been constructed. Some authors have suggested using the stability region for the construction of optimal methods. As is known, there are some stable methods whose stability region reduces to a single point; that is, the stability region has zero measure. Usually, predictor-corrector type methods are used to expand the stability region. Here, it is shown how optimal methods can be applied to solve initial-value problems for Volterra integro-differential equations. The case where the kernel of the integral is a degenerate function is considered, and special numerical methods are constructed for its solution, with their advantages demonstrated.