Diffusion Models (DMs) represent a significant advancement in image Super-Resolution (SR), aligning technical image quality more closely with human preferences and expanding SR applications. DMs address critical limitations of previous methods, enhancing overall realism and details in SR images. However, DMs suffer from color-shifting issues, and their high computational costs call for efficient sampling alternatives, underscoring the challenge of balancing computational efficiency and image quality. This survey gives an overview of DMs applied to image SR and offers a detailed analysis that underscores the unique characteristics and methodologies within this domain, distinct from broader existing reviews in the field. It presents a unified view of DM fundamentals and explores research directions, including alternative input domains, conditioning strategies, guidance, corruption spaces, and zero-shot methods. This survey provides insights into the evolution of image SR with DMs, addressing current trends, challenges, and future directions in this rapidly evolving field.