The assembly of DNA from small fragments into large constructs has seen significant recent development, becoming a pivotal technology in the ability to implement the vision of synthetic biology. As the cost of whole gene synthesis is decreasing, whole genome synthesis at the other end of the spectrum has expanded our horizons to the prospect of fully engineered synthetic cells. However, the recently proven ability to synthesise genome-scale DNA is at odds with our ability to rationally engineer biological devices, which lags significantly behind. Most work in synthetic biology takes place on an intermediate scale with the combinatorial construction of networks and metabolic pathways from registries of modular biopart components. Implementation for rapid prototyping of engineered biological circuits requires quick and reliable DNA assembly according to specific architectures. It is apparent that DNA assembly is now a limiting technology in advancing synthetic biology. Current techniques employ standardised restriction enzyme assembly protocols such as BioBricks™, BglBricks and Golden Gate methods. Alternatively, sequence-independent overlap techniques, such as In-Fusion™, SLIC and Gibson isothermal assembly are becoming popular for larger assemblies, and in vivo DNA assembly in yeast and bacillus appears adept for chromosome fabrication. It is important to consider how the use of different technologies may impact the outcome of a construction, since the assembly technique can direct the architecture and diversity of systems that can be made. This review provides a critical examination of recent DNA assembly strategies and considers how this important facilitating aspect of synthetic biology may proceed in the future.