Artificial Intelligence (AI) provides an interesting set of techniques to support the design of cryptographic primitives, especially in the symmetric setting. Indeed, several steps in the design of symmetric ciphers can be formulated as optimization problems, that can be solved in turn through nature-inspired optimization methods such as evolutionary algorithms. Further, certain low-level components in symmetric ciphers can also be implemented by computational models traditionally studied in the area of AI and natural computing, such as cellular automata. In this talk, we give an overview of such AI methods proposed in the literature to construct cryptographic primitives, focusing on the use cases of pseudorandom generators, Boolean functions and S-boxes. We conclude by discussing a few interesting directions of research on the design of cryptographic primitives where AI methods could be applied in the future.