We study eta-invariants of links and show that in many cases they form link concordance invariants, in particular that many eta-invariants vanish for slice links. This result contains and generalizes previous invariants by Smolinsky and Cha–Ko. We give a formula for the eta-invariant for boundary links. In several interesting cases this allows us to show that a given link is not slice. We show that even more eta-invariants have to vanish for boundary slice links.