In this chapter we investigate three subjects concerning the convexity of functions defined on a space of matrices (or just on a convex subset of it). The first one is devoted to the convex spectral functions, that is, to the convex functions F:Sym(n,R)→R">F:Sym(n,R)→RF:Sym(n,R)→R whose values F(A) depend only on the spectrum of A. The main result concerns their description as superpositions f∘Λ">f∘Λf∘Λ between convex functions f:Rn→R">f:Rn→Rf:Rn→R invariant under permutations, and the eigenvalues map Λ">ΛΛ.