  Let $g$ be a classical Lie algebra, i.e., either $gl_n$, $sp_n$, or $so_n$
and let $e\in g$ be a nilpotent element. We study various properties of
centralisers $g_e$. The first four sections deal with rather elementary
questions, like the centre of $g_e$, commuting varieties associated with $g_e$,
or centralisers of commuting pairs. The second half of the paper addresses
problems related to different Poisson structures on $g_e^*$ and symmetric
invariants of $g_e$.
