Natural computing is an interdisciplinary research field that encompasses two main areas: the use of computational models drawing inspiration from natural processes to solve problems relevant to computer science, and the study of natural phenomena in terms of information processing. In this talk, we focus on the first research strand by discussing several results where natural computing techniques are employed to design cryptographic primitives. In particular, we present two main research lines, the first one centering on the use of Evolutionary Algorithms for constructing Boolean functions and S-boxes with good cryptographic properties, as well as other related combinatorial designs, and the second one which considers the secret sharing schemes arising from Cellular Automata. For both research lines we give a broad overview of the results obtained in the past two years, and frame them in perspective by discussing some new open problems and challenges to be tackled in the future.