The self-assembly of molecular building blocks into one-dimensional supramolecular architectures has opened up new frontiers in materials science. Due to the noncovalent interactions between the monomeric units, these architectures are intrinsically dynamic, and understanding their kinetic driving forces is key to rationally programming their morphology and function. To understand the self-assembly dynamics of supramolecular polymerizations (SP), kinetic models based on aggregate growth by sequential monomer association and dissociation have been analyzed. However, fragmentation and coagulation events can also play a role, as evident from studies on peptide self-assembly and the fact that aggregations can be sensitive to mechanical agitations. Here, we analyze how fragmentation and coagulation events influence SP kinetics by theoretical analysis of self-assembling systems of increasing complexity. Our analysis starts with single-component systems in which aggregates are able to grow via an isodesmic or cooperative nucleation-elongation mechanism. Subsequently, equilibration dynamics in cooperative two-component supramolecular copolymerizations are investigated. In the final part, we reveal how aggregate growth in the presence of competing, kinetically controlled pathways is influenced by fragmentation and coagulation reactions and reveal how seed-induced growth can give rise to block copolymers. Our analysis shows how fragmentation and coagulation reactions are able to modulate SP kinetics in ways that are highly system dependent.