  A disordered system is denominated `annealed' when the interactions
themselves may evolve and adjust their values to lower the free energy. The
opposite (`quenched') situation when disorder is fixed, is the one relevant for
physical spin-glasses, and has received vastly more attention. Other problems
however are more natural in the annealed situation: in this work we discuss
examples where annealed averages are interesting, in the context of matrix
models. We first discuss how in practice, when system and disorder adapt
together, annealed systems develop `planted' solutions spontaneously, as the
ones found in the study of inference problems. In the second part, we study the
probability distribution of elements of a matrix derived from a rotationally
invariant (not necessarily Gaussian) ensemble, a problem that maps into the
annealed average of a spin glass model.
