DNA-joining by ligase and polymerase enzymes has provided the foundational tools for generating recombinant DNA and enabled the assembly of gene and genome-sized synthetic products. Xenobiotic nucleic acid (XNA) analogues of DNA and RNA with alternatives to the canonical bases, so-called 'unnatural' nucleobase pairs (UBP-XNAs), represent the next frontier of nucleic acid technologies, with applications as novel therapeutics and in engineering semi-synthetic biological organisms. To realise the full potential of UBP-XNAs, researchers require a suite of compatible enzymes for processing nucleic acids on a par with those already available for manipulating canonical DNA. In particular, enzymes able to join UBP-XNA will be essential for generating large assemblies and also hold promise in the synthesis of single-stranded oligonucleotides. Here, we review recent and emerging advances in the DNA-joining enzymes, DNA polymerases and DNA ligases, and describe their applications to UBP-XNA manipulation. We also discuss the future directions of this field which we consider will involve two-pronged approaches of enzyme biodiscovery for natural UBP-XNA compatible enzymes, coupled with improvement by structure-guided engineering.