Recently, state-space deep learning models, particularly Mamba, have emerged as a better alternative to transformers for various NLP and computer vision applications due to their ability to model long-range sequences with linear-time computational complexity. Such models are proven to be efficient for various image restoration applications including single image super resolution (SISR). This paper surveys the recent developments in SISR using state space based models and make a performance comparison of these models and their architectural complexities. Since these architectures have significantly lower computational and memory requirements compared to global attention-based models, many lightweight variants have been proposed for real-time deployment on edge devices. This study explores such lightweight Mamba-based architectures for efficient super-resolution reconstruction and also discusses the future potential of state-space model (SSM)-based approaches.