There has been significant success recently in proving that unital simple C*-algebras are Z-stable, under other regularity hypotheses. With certain new techniques (particularly concerning traces and algebraic simplicity), many of these results can be generalized to the nonunital setting. In particular, it can be shown that the following C*-algebras are Z-stable: (i) (nonunital) ASH algebras with slow dimension growth (T-Toms); (ii) (nonunital) C*-algebras with finite nuclear dimension (T); and (iii) (nonunital) C*-algebras with strict comparison and finitely many extreme traces (Nawata). I will discuss the proofs of these results, with emphasis on the innovations required for the nonunital setting.