The question of how syntactic structure can be built at the neural level has come to the forefront of cognitive neuroscience in the last decade. Neural oscillations have been widely recognised as playing an important role in building syntactic representations. In this talk I will review existing oscillatory approaches to syntactic structure building and assess their functionality in light of basic properties of a hierarchical syntactic structure, such as varied length of syntactic phrases, nesting of constituents, overlap in length between different levels of the syntactic hierarchy and others. I will also briefly discuss key requirements on neural structure building mechanisms from the perspective of a real-time parser.