  Some recent results concerning the Sherrington-Kirkpatrick model are
reported. For $T$ near the critical temperature $T_c$, the replica free energy
of the Sherrington-Kirkpatrick model is taken as the starting point of an
expansion in powers of $\delta Q_{ab} = (Q_{ab} - Q_{ab}^{\rm RS})$ about the
Replica Symmetric solution $Q_{ab}^{\rm RS}$. The expansion is kept up to 4-th
order in $\delta{\bm Q}$ where a Parisi solution $Q_{ab} = Q(x)$ emerges, but
only if one remains close enough to $T_c$.
  For $T$ near zero we show how to separate contributions from $x\ll T\ll 1$
where the Hessian maintains the standard structure of Parisi Replica Symmetry
Breaking with bands of eigenvalues bounded below by zero modes. For $T\ll x
\leq 1$ the bands collapse and only two eigenvalues, a null one and a positive
one, are found. In this region the solution stands in what can be called a {\sl
droplet-like} regime.
