Continuous directed evolution methods allow the key steps of evolution-gene diversification, selection, and replication-to proceed in the laboratory with minimal researcher intervention. As a result, continuous evolution can find solutions much more quickly than traditional discrete evolution methods. Continuous evolution also enables the exploration of longer and more numerous evolutionary trajectories, increasing the likelihood of accessing solutions that require many steps through sequence space and greatly facilitating the iterative refinement of selection conditions and targeted mutagenesis strategies. Here we review the historical advances that have expanded continuous evolution from its earliest days as an experimental curiosity to its present state as a powerful and surprisingly general strategy for generating tailor-made biomolecules, and discuss more recent improvements with an eye to the future.