Machining processes produce unwanted remainders of material on the free edges which are called burrs. In particular, the drilling process generates an entry burr and a typically larger exit burr. When drilling stacks of several workpieces, exit and entry burrs are produced simultaneously at the interfaces. The presence of burrs can degrade the static and fatigue strength of the parts and assemblies containing them. An example concerns the burrs formed at the interface during the drilling of multistacks in One-Way-Assembly processes, where deburring is not systematically applied. The effect on fatigue can be significant. Reductions of up to 70% in fatigue life have been reported, even though the explanatory rationale is not clear. This article reviews existing works on burrs, focusing on drilling burrs. A description of the morphology of different types of burrs and of measurement technologies is given. Burr formation mechanisms and their modeling are reviewed. Burr control strategies and the main deburring technologies are examined. The limited literature on the effects of burrs on the static and fatigue strength of mechanical assemblies is also explored.