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Watson-Crick L systems are string generating formal models obtained by augmenting Lindenmayer systems with the Watson-Crick morphism inspired by the Watson-Crick complementarity principle. The Watson-Crick morphism is controlled by a trigger—a boolean condition eventually met by the generated word. Despite their simplicity, Watson-Crick (D)0 L systems have interesting mathematical properties, a strong generative power, and they can also characterize some open decision problems. Furthermore, networks of Watson-Crick D0L systems are capable of trading space for time, and thus of characterizing linear time solutions to intractable problems. We provide a survey of results in this field since its origin in 1997 to the present, and we conclude with a series of open research problems and ideas.