In this talk we shall describe recent joint work with Peter Crooks. It is based on the observation that if a semisimple complex Lie group $G$ acts in a Hamiltonian fashion on a Poisson variety $X$, then the moment map preimage of a Slodowy slice in $\mathrm{Lie}(G)$ carries a natural Poisson structure, which is log-symplectic if $X$ is log-symplectic. We discuss how the standard family of Hessenberg varieties $\mathrm{Hess}(H)$ associated with $G$ of adjoint type can be interpreted in terms of the above construction. As a consequence we obtain, for any $x\in \mathrm{Lie}(G)$, a natural embedding of the Hessenberg variety $\mathrm{Hess}(x,H)$ into the wonderful compactification of $G$, building on results of Balibanu.