  Recent trends of ab initio studies and progress in methodologies for
electronic structure calculations of strongly correlated electron systems are
discussed. The interest for developing efficient methods is motivated by recent
discoveries and characterizations of strongly correlated electron materials and
by requirements for understanding mechanisms of intriguing phenomena beyond a
single-particle picture. A three-stage scheme is developed as renormalized
multi-scale solvers (RMS) utilizing the hierarchical electronic structure in
the energy space. It provides us with an ab initio downfolding of the global
band structure into low-energy effective models followed by low-energy solvers
for the models. The RMS method is illustrated with examples of several
materials. In particular, we overview cases such as dynamics of semiconductors,
transition metals and its compounds including iron-based superconductors and
perovskite oxides, as well as organic conductors of kappa-ET type.
