Large language models (LLMs) are solidifying their position in the modern world as effective tools for the automatic generation of text. Their use is quickly becoming commonplace in fields such as education, healthcare, and scientific research. There is a growing need to study the linguistic features present in AI-generated text, as the increasing presence of such texts has profound implications in various disciplines such as corpus linguistics, computational linguistics, and natural language processing. Many observations have already been made, however a broader synthesis of the findings made so far is required to provide a better understanding of the topic. The present survey paper aims to provide such a synthesis of extant research. We categorize the existing works along several dimensions, including the levels of linguistic description, the models included, the genres analyzed, the languages analyzed, and the approach to prompting. Additionally, the same scheme is used to present the findings made so far and expose the current trends followed by researchers. Among the most-often reported findings is the observation that AI-generated text is more likely to contain a more formal and impersonal style, signaled by the increased presence of nouns, determiners, and adpositions and the lower reliance on adjectives and adverbs. AI-generated text is also more likely to feature a lower lexical diversity, a smaller vocabulary size, and repetitive text. Current research, however, remains heavily concentrated on English data and mostly on text generated by the GPT model family, highlighting the need for broader cross-linguistic and cross-model investigation. In most cases authors also fail to address the issue of prompt sensitivity, leaving much room for future studies that employ multiple prompt wordings in the text generation phase.