  The work that Peter Schuck and I carried out during the nineties in
collaboration with the Lyon and Darmstadt theory groups is summarized. I
retrace how our theoretical developments combined with experimental results
concerning the in-medium modification of the pion-pion interaction allowed a
clarification of the chiral status of the sigma meson introduced in
relativistic theories of nuclear matter. This enabled us to build a
relativistic chiral theory, now called the chiral confining model of nuclear
matter, which includes the effect of the nucleon substructure, namely the
response of the nucleon to the nuclear scalar field generating an efficient and
natural contribution to the saturation mechanism. Using parameters from a
QCD-connected version of the chiral confining model, I describe the relative
roles of the chiral scalar field and two-pion (or two-rho) exchange for the
in-medium $NN$ attractive interaction and the associated sources of three-body
interactions needed for the saturation mechanism.
