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The idea of creating artifacts that evolve by themselves has been at the heart of the Artificial Life research, dating back to the early motives of John von Neumann’s monumental work on self-reproducing automata in the 1940’s. This vein of research is unique and fundamentally different from other more widely studied evolutionary computation research, because basic processes of evolution (heredity, variation, selection) are not given a priori as built-in mechanisms but they need to emerge as a result of interactions among microscopic components. In this talk, I will provide a brief review of how this problem has been approached in ALife using various kinds of methodologies, including classic frameworks (e.g., cellular automata, evolving programs) and more modern ones (e.g., artificial chemistry, AI/ML). I aim to highlight several key ingredients in order for complex systems to show spontaneous evolutionary behaviors by themselves and, in particular, to exhibit open-ended exploration of…