The emergence of collective motion among interacting, self-propelled agents is a central paradigm in non-equilibrium physics. Examples of such active matter range from swimming bacteria and cytoskeletal motility assays to synthetic self-propelled colloids and swarming microrobots. Remarkably, the aggregation capabilities of many of these systems rely on a theme as fundamental as it is ubiquitous in nature: communication. Despite its eminent importance, the role of communication in the collective organization of active systems is not yet understood. Here we report on the multi-scale self-organization of interacting self-propelled agents that locally process information transmitted between them by chemical signals. We show that this communication capacity greatly expands their ability to form complex structures, allowing them to self-organize through a series of collective dynamical states at multiple hierarchical levels. Our findings provide insights into the role of self-sustained signal processing for self-organization in biological systems, and open routes to applications using chemically driven colloids or microrobots.