In practice, integer quadratic optimization problems are usually solved by branch-and-bound algorithms. The main ingredients of such algorithms are dual bounds that are often derived from tractable relaxations of the problem. On the one hand, the resulting bounds should be as tight as possible, on the other hand they should be computed quickly. Clearly, there is a trade-off between these objectives. In our talk, we give an overview over recent approaches for computing dual bounds, including linearization and convexification techniques making use of linear or semidefinite programming relaxations. We also present a new approach using non-convex relaxations that does not require any linearization.