Over the past few years an animated debate has been ongoing on the role played by evolutionary perspectives opened on language and in particular on language change (cf. Croft 2000, Ritt 2004, McMahon and McMahon 2013, Norde and Van de Felde 2016, among many others). In this light, concepts and methods developed in evolutionary biology have been shown to provide innovative perspectives on the issue of both language evolution and change. In particular, in this lecture the attempt will be made to integrate the conceptual pair of so-called adaptations and exaptations into the current linguistic epistemology. In this vein, adaptive changes are characterized as responding to a general design of economy and plasticity, while exaptive changes result from the refunctionalization of (partially pre-adapted) linguistic material (cf. Gaeta 2016). On the basis of this theoretical background, the issue of possible fossils dig out in our historical languages will be discussed. Under fossils the occurrence of linguistic structure is meant which can be considered simple or primitive according to its behavioral properties with regard to the higher complexity observed in a full-blown linguistic system (cf. Bickerton 1990, Progovac 2015). Similar to classical examples drawn from evolutionary biology such as the Gouldian panda’s thumb, fossils are of particular relevance because they can reveal the scaffolding of a primitive proto-language on which full-blown linguistic systems are based (cf. Jackendoff 1999, 2009, Gaeta 2008). At the same time, their integration into the actual systems can help us understand much of the evolutionary path leading from proto-language to language.