The number of Language Models (LMs) dedicated to processing scientific text is on the rise. Keeping pace with the rapid growth of scientific LMs (SciLMs) has become a daunting task for researchers. To date, no comprehensive surveys on SciLMs have been undertaken, leaving this issue unaddressed. Given the constant stream of new SciLMs, appraising the state-of-the-art and how they compare to each other remain largely unknown. This work fills that gap and provides a comprehensive review of SciLMs, including an extensive analysis of their effectiveness across different domains, tasks and datasets, and a discussion on the challenges that lie ahead.