Meiotic crossing over is the main mechanism for constructing a new allelic composition of individual chromosomes and is necessary for the proper distribution of homologous chromosomes between gametes. The parameters of meiotic crossing over that have developed in the course of evolution are determined by natural selection and do not fully suit the tasks of selective breeding research. This review summarizes the results of experimental studies aimed at increasing the frequency of crossovers and redistributing their positions along chromosomes using genetic manipulations at different stages of meiotic recombination. The consequences of inactivation and/or overexpression of the SPO11 genes, the products of which generate meiotic double-strand breaks in DNA, for the redistribution of crossover positions in the genome of various organisms are discussed. The results of studies concerning the effect of inactivation or overexpression of genes encoding RecA-like recombinases on meiotic crossing over, including those in cultivated tomato (Solanum lycopersicum L.) and its interspecific hybrids, are summarized. The consequences of inactivation of key genes of the mismatch repair system are discussed. Their suppression made it possible to significantly increase the frequency of meiotic recombination between homeologues in the interspecific hybrid yeast Saccharomyces cerevisiae × S. paradoxus and between homologues in arabidopsis plants (Arabidopsis thaliana L.). Also discussed are attempts to extrapolate these results to other plant species, in which a decrease in reproductive properties and microsatellite instability in the genome have been noted. The most significant results on the meiotic recombination frequency increase upon inactivation of the FANCM, TOP3α, RECQ4, FIGL1 crossover repressor genes and upon overexpression of the HEI10 crossover enhancer gene are separately described. In some experiments, the increase of meiotic recombination frequency by almost an order of magnitude and partial redistribution of the crossover positions along chromosomes were achieved in arabidopsis while fully preserving fecundity. Similar results have been obtained for some crops.