The major hallmark of Alzheimer's disease is the deposition of plaques of amyloid fibrils formed from amyloid-beta (A beta) peptides. Kinetic studies have contributed significantly towards a mechanistic understanding of amyloid fibril self-assembly, however dynamic features of the aggregation process cannot be captured using ensemble methods. Here we present an assay for imaging A beta 42 aggregation dynamics at the single fibril level, allowing for the quantitative extraction of concentration and temperature dependent kinetic parameters. From direct observation of elongation using TIRF and super-resolution optical microscopy, we find that A beta 42 fibril growth is strongly polarized, with fast and slow growing ends arising from different elongation rates, but also from a growth incompetent state, which dominates the process at the slow growing end. Our findings reveal the surprising complexity of the A beta 42 fibril elongation reaction at the microscopic level.