Transposons are mobile genetic elements that have invaded all domains of life by moving between and within their host genomes. Due to their mobility (or transposition), transposons facilitate horizontal gene transfer in bacteria and foster the evolution of new molecular functions in prokaryotes and eukaryotes. As transposition can lead to detrimental genomic rearrangements, organisms have evolved a multitude of molecular strategies to control transposons, including genome defense mechanisms provided by CRISPR‐Cas systems. Apart from their biological impacts on genomes, DNA transposons have been leveraged as efficient gene insertion vectors in basic research, transgenesis and gene therapy. However, the close to random insertion profile of transposon‐based tools limits their programmability and safety. Despite recent advances brought by the development of CRISPR‐associated genome editing nucleases, a strategy for efficient insertion of large, multi‐kilobase transgenes at user‐defined genomic sites is currently challenging. The discovery and experimental characterization of bacterial CRISPR‐associated transposons (CASTs) led to the attractive hypothesis that these systems could be repurposed as programmable, site‐specific gene integration technologies. Here, we provide a broad overview of the molecular mechanisms underpinning DNA transposition and of its biological and technological impact. The second focus of the article is to describe recent mechanistic and functional analyses of CAST transposition. Finally, current challenges and desired future advances of CAST‐based genome engineering applications are briefly discussed.