Formal and explicit descriptions of natural phenomena are an essential component of any research program. The absence of such accounts significantly weaken empirical studies and often results in failure to integrate their findings into a larger cohesive whole. Although formal models of the structure of linguistic representations (i.e., syntax) have existed for decades, their acceptance and integration into other domains of language science has to date only been marginally successful. In this talk, I take a closer look at the structural properties of filler-gap dependencies (ex. [What]i did John say that Sarah would like to eat __i?), where two elements – here the filler (what) and the gap (indicated by the open slot) – that go together in meaning can occur arbitrarily far away from each other in syntactic structure. I summarize current research on constraints on extraction (also known as island phenomena), with a particular focus on the potential of satiation effects, where continued exposure to particular structures can lead to an amelioration of their ill-formedness. This presentation highlights the central importance of formal approaches to the structure of language, while also exposing shortcomings in current syntactic theorizing.