Dependency syntax represents the structure of a sentence as a tree composed of dependencies, i.e., directed relations between lexical units. While in its more general form any such tree is allowed, in practice many are not plausible or are very infrequent in attested language. This has motivated a search for constraints characterizing subsets of trees that better fit real linguistic phenomena, providing a more accurate linguistic description, faster parsing or insights on language evolution and human processing. Projectivity is the most well-studied such constraint, but it has been shown to be too restrictive to represent some linguistic phenomena, especially in flexible-word-order languages. Thus, a variety of constraints have been proposed to seek a realistic middle ground between the limitations of projectivity and the excessive leniency of unrestricted dependency structures.