Studying early language development has been a challenging task throughout the years. Earlier studies mostly documented language competence only after toddlers had started producing their first words. Theoretical and methodological advances in this domain brought about more sophisticated ways of probing into early development by exploiting overt infant behaviour. One such method is based on so-called non-nutritive sucking (NNS), namely that infants spontaneously produce rhythmic mouth movements in the absence of receiving nutrition. This behaviour has been used to investigate infants' preference and discriminatory abilities by means of the high-amplitude sucking-procedure (HAS), which initially was one of few ways to gain insight into young infants' language processing. Here, the method is described, and some key findings are highlighted together with overarching trends. Over the last decades, however, the popularity of such studies has been declining, and some potential reasons for this decline are discussed. Next, the method's relevance for contemporary research is discussed by advocating a shift from using NNS as an indirect measure of language processing towards focusing on speech production. This is seen in light of the growing literature on neural synchronisation to speech and the role of the auditory-motor coupling in speech perception.