  This is a semi-pedagogical review of a medium size on the exact determination
of and the role played by the low energy effective prepotential ${\cal F}$ in
QFT with (broken) extended supersymmetry, which began with the work of Seiberg
and Witten in 1994. While paying an attention to an overall view of this
subject lasting long over the two decades, we probe several corners marked in
the three major stages of the developments, emphasizing uses of the deformation
theory on the attendant Riemann surface as well as its close relation to matrix
models. Examples picked here in different contexts tell us that the effective
prepotential is to be identified as the suitably defined free energy $F$ of a
matrix model: ${\cal F} = F$. To be submitted to PTEP as an invited review
article and based in part on the talk delivered by one of the authors (H.I.) in
the workshop held at Shizuoka University, Shizuoka, Japan, on December 5, 2014.
