  We present some long-range interaction models for phase coexistence which
have recently appeared in the literature, recalling also their relation to
classical interface and capillarity problems. In this note, the main focus will
be on the $\Gamma$-convergence methods, emphasizing similarities and
differences between the classical theory and the new trends of investigation.
  In doing so, we also obtain some new, more precise $\Gamma$-convergence
results in terms of "interior" and "exterior" contributions. We also discuss
the structural differences between $\Gamma$-limits and "pointwise" limits,
especially concerning the "boundary terms".
