Their base is the substantial recent progress made in the understanding of cerium-based heavy-fermion (HF) materials, in terms of the single-impurity limit. Their first thrust will focus on the new characteristics that arise upon formation of a regular Ce lattice, and how the thermodynamics and transport are affected by inter-site magnetic correlations. It is known that there exist significant differences between the Ce and uranium families. Their research will concentrate on those aspects of U-based HFs with especially strong deviations from the single-ion, Kondo-like behavior of their Ce counterparts.