The goal of this contribution is to deepen the knowledge of French cleft sentences through the study of a special category of clefts called adverbial clefts. The issues that it will address concern their form, discourse frequency and boundaries with resembling structures. In order to shed light on these issues, it starts by defining the concept of adverbial from a morphosyntactic and functional point of view. It then presents a corpus-based description of the categories of adverbials that can be cleaved. Finally, it proposes a general semantic principle capable of describing and explaining, in a coherent and unitary way, both the data obtained in the empirical study and found in the form of constructed examples in the existing literature. In addition to explaining why certain adverbials can be cleaved while others cannot, this principle also allows for a distinction to be made between two syntactic realizations of the structure ‘c’est Adv que p’, as well as for a solution to the controversial issue of the status of domain adverbials.