Mathematical models involving ordinary differential equation (ODEs) arise in many diverse applications, such as fluid flows, physics-based animation, mechanical systems, mathematical finances, or chemical reaction. The realistic simulation of these applications depends on fast methods for the numerical solution of ODEs as well as adequate parallel computation schemes exploiting the potential parallelism in an optimal way. Due to the advent of multicore technology, parallel resources are now widely available in form of multicore processors or clusters. It is required to revisit parallel computation schemes of ODE solvers for the use on these multicore platforms. The objective of this article is a survey and classification of computational techniques for the numerical integration of ODE systems. The emphasis lies on a computational model which captures the specifics of ODE codes as well as a hierarchical architectural model of multicore systems.