Diffusion Models (DMs) have revolutionized the field of image Super-Resolution (SR), enhancing the quality of low-resolution (LR) images to match or exceed human perceptual standards. Despite their promising results, DMs also present new challenges such as high computational demands, lack of explainability, and color shifts. This survey provides a comprehensive overview of the theoretical foundations and methodologies of DMs applied to SR, addressing common issues and highlighting unique characteristics. It covers the evolution of DMs, including Denoising Diffusion Probabilistic Models (DDPMs), Score-based Generative Models (SGMs), and Stochastic Differential Equations (SDEs), and explores their applications in various domains. The survey also discusses efficient sampling techniques, alternative input domains, conditioning methods, guidance mechanisms, and zero-shot learning approaches. By offering a detailed analysis of current trends and future research directions, this survey aims to inspire further innovation in image SR with DMs.Diffusion Models (DMs) have revolutionized the field of image Super-Resolution (SR), enhancing the quality of low-resolution (LR) images to match or exceed human perceptual standards. Despite their promising results, DMs also present new challenges such as high computational demands, lack of explainability, and color shifts. This survey provides a comprehensive overview of the theoretical foundations and methodologies of DMs applied to SR, addressing common issues and highlighting unique characteristics. It covers the evolution of DMs, including Denoising Diffusion Probabilistic Models (DDPMs), Score-based Generative Models (SGMs), and Stochastic Differential Equations (SDEs), and explores their applications in various domains. The survey also discusses efficient sampling techniques, alternative input domains, conditioning methods, guidance mechanisms, and zero-shot learning approaches. By offering a detailed analysis of current trends and future research directions, this survey aims to inspire further innovation in image SR with DMs.