I will present a joint work with Frédéric Robert on the existence of blowing-up families of sign-changing solutions for elliptic pdes of scalar curvature type on compact manifolds. Our results complete previous results of existence and non-existence of blowing-up solutions and allow to give a complete picture for the question of compactness/non-compactness of scalar curvature type equations. In particular, I will show how the picture for sign-changing blow-up differs from the case of positive solutions.