Emotion cognition in large language models (LLMs) is crucial for enhancing performance across various applications, such as social media, human-computer interaction, and mental health assessment. We explore the current landscape of research, which primarily revolves around emotion classification, emotionally rich response generation, and Theory of Mind assessments, while acknowledge the challenges like dependency on annotated data and complexity in emotion processing. In this paper, we present a detailed survey of recent progress in LLMs for emotion cognition. We explore key research studies, methodologies, outcomes, and resources, aligning them with Ulric Neisser's cognitive stages. Additionally, we outline potential future directions for research in this evolving field, including unsupervised learning approaches and the development of more complex and interpretable emotion cognition LLMs. We also discuss advanced methods such as contrastive learning used to improve LLMs' emotion cognition capabilities.