The term ‘genomic disorder’ refers to a disease that is caused by an alteration of the genome that results in complete loss, gain or disruption of the structural integrity of a dosage sensitive gene(s). In most of the common chromosome deletion/duplication syndromes, the rearranged genomic segments are flanked by large (usually >10 kb), highly homologous low copy repeat (LCR) structures that can act as recombination substrates. Recombination between non-allelic LCR copies, also known as non-allelic homologous recombination, can result in deletion or duplication of the intervening segment. Recent findings suggest that other chromosomal rearrangements, including reciprocal, Robertsonian and jumping translocations, inversions, isochromosomes and small marker chromosomes, may also involve susceptibility to rearrangement related to genome structure or architecture. In several cases, LCRs, AT-rich palindromes and pericentromeric repeats are located at such rearrangement breakpoints. Analysis of the products of recombination at the junctions of the rearrangements reveals both homologous recombination and non-homologous end joining as causative mechanisms. Thus, a more global concept of genomic disorders emerges in which susceptibility to rearrangements occurs due to underlying complex genomic architecture. Interestingly, this architecture plays a role not only in disease etiology, but also in primate genome evolution. In this review, we discuss recent advances regarding general mechanisms for the various rearrangements of our genome, and potential models for rearrangements with non-homologous breakpoint regions.