In animal breeding, prediction of genetic effects is usually obtained through the use of mixed models. For any of these genetic effects, mixed models require the inversion of the covariance matrix associated to that effect, which is equal to the associated relationship matrix times the associated component of the genetic variance. Given the size of many genetic evaluation systems, computing the inverses of these relationship matrices is not trivial. In this review, we aim to cover computational techniques that ease inversion of relationship matrices used in animal breeding for prediction of the following different types of genetic effects: additive effect, gametic effect, effect due to presence of marked quantitative trait loci, dominance effect and different epistasis effects. Construction rules and inversion algorithms are detailed for each relationship matrix. In the final discussion, we draw up a common theoretical frame to most of the reviewed techniques. Two computational constraints come out of this theoretical frame: setting up the matrix of dependencies between levels of the effect and setting up some parts (diagonal or block-diagonal elements) of the relationship matrix to be inverted.