In the present article, we review recent computational investigations on the properties of ring polymers in solution. In particular, we focus on effective interactions obtained by means of coarse-graining techniques. We discuss the relative importance of the self-avoidance and the topological contributions in the qualitative features of the effective potential. We extend our previous results on identical rings and determine the effective potential between dissimilar ring polymers of distinct topology and size. The results obtained reveal the dramatic effects of the specific topology on the effective interactions, and hence in the structural correlations, of polymeric systems.