  This manuscript is based on the Summary and Overview talk given at the "The
International Conference of Strongly Correlated Electronic Systems" (SCES '04),
July 26-30, at Karlsruhe, Germany. After highlighting some of the principal new
experimental developments in heavy fermions presented at the conference, I turn
to two kinds of theoretical questions. (1) What is understood of the
fermi-liquid state of the heavy fermions and what is not, but may reasonably
well be understood by systematic calculations. (2) The profound issues raised
by the observed correlations near the quantum critical points in the heavy
fermions. The numbers and letters in the parenthesis in the text refer to the
listing of the talks in the "Program and Abstracts" book of the conference.
