Eutectic Ag3Sn can grow with a variety of morphologies depending on the solidification conditions and plays an important role in the performance of Pb-free solders. Here, we study morphology transitions in the β-Sn + Ag3Sn eutectic at increasing growth velocity using a combination of real-time X-ray imaging and analytical electron microscopy. Orthorhombic Ag3Sn grew as faceted plates or rods with [010] growth direction and (001) as the largest facet in all three eutectic growth morphologies: Irregular plate, broken-lamellar, and rod. Reproducible β-Sn + Ag3Sn orientation relationships formed for the latter two morphologies. The mechanisms of spacing adjustment and the reversible transition from plate to rod growth are studied for transient solidification after velocity changes. The transition from fully eutectic growth to β-Sn dendrites plus eutectic is reasonably reproduced using a competitive growth criterion. At the highest velocities, Ag3Sn rods developed perturbations whose break down into particles is discussed in terms of unsteady growth and pinch-off mechanisms.