Knowledge of language, its structure and grammar are an essential part of our education and daily activities. Despite the importance of language in our lives, linguistic theories that explain how the language system operates are often disconnected from our knowledge of the brain’s neurocognitive mechanisms underpinning the linguistic function. This is reflected, for example, in the inclusion of abstract and often controversial elements into theories of language. Here, we discuss the case of the so-called null constituent and its smallest and the most controversial variant – the zero morpheme, a hypothetical morphosyntactic device that has no overt physical (phonological or orthographic) expression. Focusing on the putative inflectional zero morpheme, we discuss the theoretical origins and pitfalls of this approach and advocate the important role for neurobiological research that could try to elucidate the neurocognitive reality of such constructs in linguistic communication.