This paper presents a detailed examination of Group Key Establishment methods, pivotal in securing group communication over public networks. We classify Group Key Establishment into three key categories: classical, quantum-safe, and quantum-based, each tailored to address distinct challenges in key management, particularly under the constraints of member dynamics and resource efficiency. Highlighting the critical influence of emerging quantum technologies, our study emphasizes the growing importance of quantum-resistant approaches to safeguard group communications against quantum threats. This paper traverses the evolution of Group Key Establishment protocols, shedding light on the shifting cryptographic paradigms and future prospects in the era of quantum advancement.