Stance detection is essential for understanding subjective content across various platforms such as social media, news articles, and online reviews. Recent advances in Large Language Models (LLMs) have revolutionized stance detection by introducing novel capabilities in contextual understanding, cross-domain generalization, and multimodal analysis. Despite these progressions, existing surveys often lack comprehensive coverage of approaches that specifically leverage LLMs for stance detection. To bridge this critical gap, our review article conducts a systematic analysis of stance detection, comprehensively examining recent advancements of LLMs transforming the field, including foundational concepts, methodologies, datasets, applications, and emerging challenges. We present a novel taxonomy for LLM-based stance detection approaches, structured along three key dimensions: 1) learning methods, including supervised, unsupervised, few-shot, and zero-shot; 2) data modalities, such as unimodal, multimodal, and hybrid; and 3) target relationships, encompassing in-target, cross-target, and multi-target scenarios. Furthermore, we discuss the evaluation techniques and analyze benchmark datasets and performance trends, highlighting the strengths and limitations of different architectures. Key applications in misinformation detection, political analysis, public health monitoring, and social media moderation are discussed. Finally, we identify critical challenges such as implicit stance expression, cultural biases, and computational constraints, while outlining promising future directions, including explainable stance reasoning, low-resource adaptation, and real-time deployment frameworks. Our survey highlights emerging trends, open challenges, and future directions to guide researchers and practitioners in developing next-generation stance detection systems powered by large language models.