The aim of this paper is to review the use of GenAI in scientometrics, and to begin a debate on the broader implications for the field. First, we provide an introduction on GenAI's generative and probabilistic nature as rooted in distributional linguistics. And we relate this to the debate on the extent to which GenAI might be able to mimic human 'reasoning'. Second, we leverage this distinction for a critical engagement with recent experiments using GenAI in scientometrics, including topic labelling, the analysis of citation contexts, predictive applications, scholars' profiling, and research assessment. GenAI shows promise in tasks where language generation dominates, such as labelling, but faces limitations in tasks that require stable semantics, pragmatic reasoning, or structured domain knowledge. However, these results might become quickly outdated. Our recommendation is, therefore, to always strive to systematically compare the performance of different GenAI models for specific tasks. Third, we inquire whether, by generating large amounts of scientific language, GenAI might have a fundamental impact on our field by affecting textual characteristics used to measure science, such as authors, words, and references. We argue that careful empirical work and theoretical reflection will be essential to remain capable of interpreting the evolving patterns of knowledge production.