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 $xll Tll 1$ where the Hessian maintains the standard structure of Parisi Replica Symmetry Breaking with bands of eigenvalues bounded below by zero modes. For $Tll x leq 1$ 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.
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