Asexual reproduction is still used by some organisms but in general failed to pass the test of natural selection. In sexual reproduction, new combinations of genes can be assembled on the same chromosomes through recombination. In addition, independent assortment during meiosis generates endless genetic diversity. This variation enables a species to overcome novel environmental changes by fast adaptive change. But in asexual reproduction, natural selection has to wait for some sort of mutation or change due to drift to take place, to act on.
Sexual reproduction can also put two beneficial mutations together (although there is always a possibility to break a favorable combination too), or eliminate a deleterious one. Overall, groups reproducing sexually can evolve more quickly than those that do not, because the combination of beneficial mutations will occur more quickly and deleterious mutations will accumulate more slowly.
So overall there are many advantages to sexual reproduction like slower rate of reproduction but faster evolution, lower extinction rates, fast removal of deleterious mutations and better adaptation to changing environment.