In the last years, tremendous progress has been achieved in the field of gene editing in plants. By the induction of single site-specific double-strand breaks (DSBs), the knockout of genes by non-homologous end joining has become routine in many plant species. Recently, the efficiency of inducing pre-planned mutations by homologous recombination has also been improved considerably. However, very little effort has been undertaken until now to achieve more complex changes in plant genomes by the simultaneous induction of several DSBs. Several reports have been published on the efficient induction of deletions. However, the induction of intrachromosomal inversions and interchromosomal recombination by the use of CRISPR/Cas has only recently been reported. In this review, we want to sum up these results and put them into context with regards to what is known about natural chromosome rearrangements in plants. Moreover, we review the recent progress in CRISPR/Cas-based mammalian chromosomal rearrangements, which might be inspiring for plant biologists. In the long run, the controlled restructuring of plant genomes should enable us to link or break linkage of traits at will, thus defining a new area of plant breeding.