Lexical semantic change (LSC) detection investigates changes in word meaning over time, focusing on language use at the lexical-semantic level from a diachronic perspective. The field has made significant progress over the past two decades, driven by the increased availability of multilingual benchmarks, notable performance improvements, and growing interdisciplinary applications. In this paper, we review the evolution of LSC models and benchmark constructions within the context of popular shared tasks. By categorizing LSC models into generations defined by key components, our investigation suggests that performance breakthroughs have been largely driven by advances in semantic representations, transitioning from count-based models to recent transformer-based approaches. Notably, transformer models have established themselves as state-of-the-art by integrating Word-in-Context tasks, which emphasize semantic proximity in context. Furthermore, we review substantial studies that primarily leverage diachronic word embeddings to explore political, social, and cultural contexts beyond the linguistic domain. Our work provides valuable insights for future model development and encourages further interdisciplinary exploration within digital humanities and social sciences.