The concept of higher-order assembly signalling or signalling by co-operative assembly formation (SCAF) was proposed based on the structures of signalling assemblies formed by proteins featuring domains from the death-fold family and the Toll/interleukin-1 receptor domain family. Because these domains form filamentous assemblies upon stimulation and activate downstream pathways through induced proximity, they were envisioned to sharpen response thresholds through the extreme co-operativity of higher-order assembly. Recent findings demonstrate that a central feature of the SCAF mechanism is the nucleation barrier that allows a switch-like, digital or 'all-or-none' response to minute stimuli. In agreement, this signalling mechanism features in cell-death and innate immunity activation pathways where a binary decision is required. Here, we broaden the concept of SCAF to encapsulate the essential kinetic properties of open-ended assembly in signalling, compare properties of filamentous assemblies and other co-operative assemblies such as biomolecular condensates, and review how this concept operates in cells.