Ever since gene targeting or specific modification of genome sequences in mice was achieved in the early 1980s, the reverse genetic approach of precise editing of any genomic locus has greatly accelerated biomedical research and biotechnology development. In particular, the recent development of the CRISPR/Cas9 system has greatly expedited genetic dissection of 3D genomes. CRISPR gene-editing outcomes result from targeted genome cleavage by ectopic bacterial Cas9 nuclease followed by presumed random ligations via the host double-strand break repair machineries. Recent studies revealed, however, that the CRISPR genome-editing system is precise and predictable because of cohesive Cas9 cleavage of targeting DNA. Here, we synthesize the current understanding of CRISPR DNA fragment-editing mechanisms and recent progress in predictable outcomes from precise genetic engineering of 3D genomes. Specifically, we first briefly describe historical genetic studies leading to CRISPR and 3D genome engineering. We then summarize different types of chromosomal rearrangements by DNA fragment editing. Finally, we review significant progress from precise 1D gene editing toward predictable 3D genome engineering and synthetic biology. The exciting and rapid advances in this emerging field provide new opportunities and challenges to understand or digest 3D genomes.