  There now exists a practical method (IP) for the routine inversion of
$S$-matrix elements to produce the corresponding potential. It can be applied
to spin-1/2 and spin-1 projectiles. We survey the ways that IP inversion can be
applied in nuclear physics by inverting $S_{lj}$ derived from theory or from
experiment. The IP inversion method can be extended to invert $S_{lj}(E)$ over
a range of energies to produce a potential $V(r,E) +
\vect{l}\vdot\gvect{\sigma} V_{\rm ls}(r,E)$. It also yields parity-dependent
potentials between pairs of light nuclei and can be convoluted with a direct
search on the $S$-matrix to produce `direct data $\to V$ inversion'. The last
is an economical alternative form of optical model search to fit many
observables (e.g. for polarized deuterons) for many energies, producing an
energy-dependent potential with many parameters (e.g. $T_{\rm R}$ for
deuterons).
