Human insulin has long been known to form amyloid fibrils under given conditions. The molecular basis of insulin aggregation is relevant for modeling the amyloidogenesis process, which is involved in many pathologies, as well as for improving delivery systems, used for diabetes treatments. Insulin aggregation displays a wide variety of morphologies, from small oligomeric filaments to huge floccules, and therefore different specific processes are likely to be intertwined in the overall aggregation. In the present work, we studied the aggregation kinetics of human insulin at low pH and different temperatures and concentrations. The structure and the morphogenesis of aggregates on a wide range of length scales (from monomeric proteins to elongated fibrils and larger aggregates networks) have been monitored by using different experimental techniques: time-lapse atomic force microscopy (AFM), quasi-elastic light-scattering (QLS), small and large angle static light-scattering, thioflavin T fluorescence, and optical microscopy. Our experiments, along with the analysis of scattered intensity distribution, show that fibrillar aggregates grow following a thermally activated heterogeneous coagulation mechanism, which includes both tip-to-tip elongation and lateral thickening. Also, the association of fibrils into bundles and larger clusters (up to tens of microns) occurs simultaneously and is responsible for an effective lag-time.