To adapt to real-world dynamics, intelligent systems need to assimilate new knowledge without catastrophic forgetting, where learning new tasks leads to a degradation in performance on old tasks. To address this, continual learning concept is proposed for enabling autonomous systems to acquire new knowledge and dynamically adapt to changing environments. Specifically, energy-efficient continual learning is needed to ensure the functionality of autonomous systems under tight compute and memory resource budgets (i.e., so-called autonomous embedded systems). Neuromorphic computing, with brain-inspired Spiking Neural Networks (SNNs), offers inherent advantages for enabling low-power/energy continual learning in autonomous embedded systems. In this paper, we comprehensively discuss the foundations and methods for enabling continual learning in neural networks, then analyze the state-of-the-art works considering SNNs. Afterward, comparative analyses of existing methods are conducted while considering crucial design factors, such as network complexity, memory, latency, and power/energy efficiency. We also explore the practical applications that can benefit from SNN-based continual learning and open challenges in real-world scenarios. In this manner, our survey provides valuable insights into the recent advancements of SNN-based continual learning for real-world application use-cases.