Audio classification is paramount in a variety of applications including surveillance, healthcare monitoring, and environmental analysis. Traditional methods frequently depend on intricate signal processing algorithms and manually crafted features, which may fall short in fully capturing the complexities of audio patterns. Neuromorphic computing, inspired by the architecture and functioning of the human brain, presents a promising alternative for audio classification tasks. This survey provides an exhaustive examination of the current state-of-the-art in neuromorphic-based audio classification. It delves into the crucial components of neuromorphic systems, such as Spiking Neural Networks (SNNs), memristors, and neuromorphic hardware platforms, highlighting their advantages in audio classification. Furthermore, the survey explores various methodologies and strategies employed in neuromorphic audio classification, including event-based processing, spike-based learning, and bio-inspired feature extraction. It examines how these approaches address the limitations of traditional audio classification methods, particularly in terms of energy efficiency, real-time processing, and robustness to environmental noise. Additionally, the paper conducts a comparative analysis of different neuromorphic audio classification models and benchmarks, evaluating their performance metrics, computational efficiency, and scalability. By providing a comprehensive guide for researchers, engineers and practitioners, this survey aims to stimulate further innovation and advancements in the evolving field of neuromorphic audio classification.