  In the first (and abstract) part of this survey we prove the unitary
equivalence of the inverse of the Krein--von Neumann extension (on the
orthogonal complement of its kernel) of a densely defined, closed, strictly
positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon
>0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator.
  This establishes the Krein extension as a natural object in elasticity theory
(in analogy to the Friedrichs extension, which found natural applications in
quantum mechanics, elasticity, etc.).
  In the second, and principal part of this survey, we study spectral
properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the
perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian)
defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and
nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a
class of nonsmooth domains which contains all convex domains, along with all
domains of class $C^{1,r}$, $r>1/2$.
