In Molecular Dynamics Simulations, typically the forces between pairs of particles are calculated. However, the inclusion of three-body forces offers the possibility of obtaining more accurate results in certain simulations. When computing the forces between all possible triplets of particles, this is in a complexity class of O(n^3), so there is interest in developing algorithms to speed this up. To date, however, few algorithms for efficient computation of three-body forces have been developed. This thesis gives a literature review of algorithms already developed and describes how they work. The literature review provides an entry point into the computation of three-body forces and is used to critically analyze the most valuable research directions in this field. The advantages and disadvantages, as well as possible use cases for different algorithms, are discussed. The implementation of three of the most promising of such algorithms for distributed memory environments is presented. All three implementations are investigated on a medium size HPC cluster for their runtime. Furthermore, one of these implementations is examined for its hit-rate and load balance, as well as its accuracy.