The recent advancements in language models have significantly catalyzed progress in computational biology. A growing body of research strives to construct unified foundation models for single-cell biology, with language models serving as the cornerstone. In this paper, we systematically review the developments in foundation language models designed specifically for single-cell biology. Our survey offers a thorough analysis of various incarnations of single-cell foundation language models, viewed through the lens of both pre-trained language models (PLMs) and large language models (LLMs). This includes an exploration of data tokenization strategies, pre-training/tuning paradigms, and downstream single-cell data analysis tasks. Additionally, we discuss the current challenges faced by these pioneering works and speculate on future research directions. Overall, this survey provides a comprehensive overview of the existing single-cell foundation language models, paving the way for future research endeavors.