Empathy, a cornerstone of human interaction, is a unique quality to humans that Large Language Models (LLMs) are believed to lack. Our study aims to review the literature on the capacity of LLMs in demonstrating empathy Methods: We conducted a literature search on MEDLINE up to July 2023. Seven publications ultimately met the inclusion criteria. Results: All studies included in this review were published in 2023. All studies but one focused on ChatGPT-3.5 by OpenAI. Only one study evaluated empathy based on objective metrics, and all others used subjective human assessment. The studies reported LLMs to exhibits elements of empathy, including emotions recognition and providing emotionally supportive responses in diverse contexts, most of which were related to healthcare. In some cases, LLMs were observed to outperform humans in empathy-related tasks. Conclusion: LLMs demonstrated some aspects of empathy in variable scenarios, mainly related to healthcare. The empathy may be considered cognitive empathy. Social skills are a fundamental aspect of intelligence, thus further research is imperative to enhance these skills in AI.