An overview is provided of the design activities and the related neutronics support efforts conducted in the European Union for the development of breeder blankets for future fusion power reactors. The EU fusion programme considers two blanket lines, the Helium-Cooled Pebble Bed (HCPB) blanket with Lithium ceramics pebbles (Li4SiO4 or Li2TiO3) as breeder and beryllium pebbles as neutron multiplier, and the Helium-Cooled Lithium-Lead (HCLL) blanket with the Pb-Li eutectic alloy as breeder and neutron multiplier. The blanket design and the related R&D efforts are based on the use of the same coolant and the same modular blanket structure to minimise the development costs as much as possible. The neutronic support efforts include design analyses for the layout and optimization of the modular HCPB/HCLL blankets based on detailed three-dimensional Monte Carlo calculations as well as underlying neutronics activities conducted in the frame of the European Fusion and Activation File (EFF/EAF) projects to develop qualified nuclear data and computational tools for reliable neutronics design calculations.