Crystallization of amorphous Fe78B13Si9 has been investigated using a combination of differential scanning calorimetry (DSC) and conventional and high-resolution transmission electron microscopy. The crystallization mechanisms and crystalline products are sensitive to the annealing temperature. At 450-degrees-C, crystallization takes place by the growth of bcc alpha-Fe (Si) dendrites, while at 510 and 515-degrees-C there are three simultaneous reactions to form dendritic bcc alpha-Fe (Si), elliptical crystals of bct Fe3B and lamellar eutectic spherulites of bcc alpha-Fe (Si) and bct Fe3B. Quantitative TEM shows that the bcc alpha-Fe (Si) dendrites and bcc alpha-Fe (Si)-bct Fe3B spherulites both form with constant nucleation and growth rates, in agreement with previous DSC measurements of an Avrami exponent of 4.