  We consider supersymmetric domain walls of four-dimensional
$\mathcal{N}\!=\!1$ $Sp(N)$ SQCD with $F\!=\!N+1$ and $F\!=\!N+2$ flavors.
  First, we study numerically the differential equations defining the walls,
classifying the solutions. When $F\!=\!N+2$, in the special case of the
parity-invariant walls, the naive analysis does not provide all the expected
solutions. We show that an infinitesimal deformation of the differential
equations sheds some light on this issue.
  Second, we discuss the $3d$ $\mathcal{N}\!=\!1$ Chern-Simons-matter theories
that should describe the effective dynamics on the walls. These proposals pass
various tests, including dualities and matching of the vacua of the massive
$3d$ theory with the $4d$ analysis. However, for $F\!=\!N+2$, the semiclassical
analysis of the vacua is only partially successful, suggesting that
yet-to-be-understood strong coupling phenomena are into play in our $3d$
$\mathcal{N}\!=\!1$ gauge theories.
