Increasing demands on function and performance call for burr-free workpiece edges after machining. Since deburring is a costly and non-value-added operation, the understanding and control of burr formation is a research topic with high relevance to industrial applications. Following a review of burr classifications along with the corresponding measurement technologies, burr formation mechanisms in machining are described. Deburring and burr control are two possible ways to deal with burrs. For both, an insight into current research results are presented. Finally, a number of case studies on burr formation, control and deburring along with their economic implications are presented.