In this talk we present bounds for the variation of the spectral radius of a graph G after some perturbations (or local vertex/edge modifications) of G. The perturbations considered here are the connection of a new vertex to, say, g vertices of G, the addition of a pendant edge (the previous case when g = 1) and the addition of an edge. The proposed method is based on continuous perturbations and the study of their associated differential inequalities. Within rather economical information (namely, the degrees of the vertices involved in the perturbation), best possible inequalities are obtained. Besides, the cases when equalities are attained are characterized. The asymptotic behaviors of the obtained bounds are also discussed.