abstract: In this talk we describe the action of the mod 2 Steenrod algebra on the cohomology of various polyhedral products and related spaces. By studying the combinatorics of underlying simplicial complexes, we deduce some consequences for the lowest cohomological dimension in which non-trivial Steenrod operations can appear. Finally, we see how non-trivial Steenrod actions on the building blocks of polyhedral products and joins propagate to these spaces themselves. The talk is based on a paper that came out as a result of a team project in the Women In Topology IV workshop.