C*-algebraic bundles (nowadays simply called Fell bundles) were introduced by Fell at the end of the sixties as yet another tool to deal with the representation theory of locally compact groups. The reason why the related literature is still growing is probably due to the fact that they fit pretty well with various aspects of the theory of (twisted) actions (and coactions) of groups (and groupoids) on C*-algebras. For instance, many familiar constructions like group C*-algebras and crossed products can be viewed as cross sectional C*-algebras of suitable Fell bundles. In the talk we will introduce the concept of positive definite "multiplier" between Fell bundles and discuss some consequences and applications. Especially, a notion of amenability for Fell bundles naturally appears. Other applications are concerned with the construction of certain functors from the category of positive definite multipliers to the category of completely positive maps between C*-algebras and with the existence of certain C*-correspondences associated to left actions of Fell bundles on right Hilbert bundles. (Joint work with E. Bedos) The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page?authuser=0