Chromosome imbalances are the leading cause of pregnancy loss in humans and play major roles in male and female infertility. Within the past two decades, the development and application of preimplantation genetic diagnosis (PGD) has played an important role in infertility practices worldwide. The purpose of this review is to discuss, how PGD may be applied in combating numerical chromosomal abnormalities and in Robertsonian and reciprocal chromosome translocations. We shall consider prevalence and risk of each aberration, interchromosomal effects and rationale behind use of PGD in each case. Numerical chromosome abnormalities (aneuploidy and polyploidy) in particular affect a very high proportion of preimplantation embryos (~ 50%). Given that a majority of preimplantation embryos are aneuploid, PGD can be used to screen embryos and transfer euploid embryos to improve pregnancy rates and reduce spontaneous abortions. The rationale of utilize PGD to transfer only euploid embryos would seem sound, but controversies exist surrounding application of PGD for aneuploidy detection. To this end, we will discuss the dichotomy between favorable descriptive reports and less favorable randomized clinical trial data. This review will discuss the trend towards differing sources of embryonic DNA (e.g. polar body vs blastomere vs blastocyst) as well as development of novel technologies for 24 chromosomes analysis.