This survey provides an overview of recent deep learning (DL) methods for single image super-resolution (SISR), focusing on two key areas: efficient neural network architectures and effective optimization objectives. SISR aims to reconstruct high-resolution (HR) images from low-resolution (LR) inputs, a challenging ill-posed problem. Traditional methods face issues such as unclear mappings between LR and HR spaces and inefficiency in complex mappings. Recent DL-based approaches have significantly improved performance by learning hierarchical representations and optimizing objectives. The survey categorizes DL-based SISR methods into two groups: efficient neural network architectures and effective optimization objectives. For each category, representative works are discussed, highlighting their contributions and experimental results. The review also identifies current challenges and future trends in DL-based SISR, emphasizing the importance of combining DL with domain knowledge. Key DL-based SISR methods include SRCNN, which uses a three-layer CNN for super-resolution. However, it has limitations, such as reliance on bicubic interpolation. FSRCNN and ESPCN address these by using subpixel convolution and efficient upsampling. VDSR, a deep CNN with 20 layers, improves performance through residual learning. DRCN and SRResNet further enhance performance by using residual blocks and multisupervised training. EDSR and MDSR achieve state-of-the-art results by using deeper networks and multiscale architectures. Optimization objectives for SISR include mean square error (MSE), mean absolute error (MAE), and Kullback-Leibler divergence (KLD). These objectives help in learning effective mappings between LR and HR spaces. Recent works have explored non-Gaussian noise models and perceptual losses to improve performance. The survey also discusses the importance of using appropriate optimization objectives for different degradation scenarios. Overall, DL-based SISR has made significant progress, with methods achieving high-quality HR images. Future research will focus on improving performance under unknown degradation and combining DL with domain-specific knowledge.This survey provides an overview of recent deep learning (DL) methods for single image super-resolution (SISR), focusing on two key areas: efficient neural network architectures and effective optimization objectives. SISR aims to reconstruct high-resolution (HR) images from low-resolution (LR) inputs, a challenging ill-posed problem. Traditional methods face issues such as unclear mappings between LR and HR spaces and inefficiency in complex mappings. Recent DL-based approaches have significantly improved performance by learning hierarchical representations and optimizing objectives. The survey categorizes DL-based SISR methods into two groups: efficient neural network architectures and effective optimization objectives. For each category, representative works are discussed, highlighting their contributions and experimental results. The review also identifies current challenges and future trends in DL-based SISR, emphasizing the importance of combining DL with domain knowledge. Key DL-based SISR methods include SRCNN, which uses a three-layer CNN for super-resolution. However, it has limitations, such as reliance on bicubic interpolation. FSRCNN and ESPCN address these by using subpixel convolution and efficient upsampling. VDSR, a deep CNN with 20 layers, improves performance through residual learning. DRCN and SRResNet further enhance performance by using residual blocks and multisupervised training. EDSR and MDSR achieve state-of-the-art results by using deeper networks and multiscale architectures. Optimization objectives for SISR include mean square error (MSE), mean absolute error (MAE), and Kullback-Leibler divergence (KLD). These objectives help in learning effective mappings between LR and HR spaces. Recent works have explored non-Gaussian noise models and perceptual losses to improve performance. The survey also discusses the importance of using appropriate optimization objectives for different degradation scenarios. Overall, DL-based SISR has made significant progress, with methods achieving high-quality HR images. Future research will focus on improving performance under unknown degradation and combining DL with domain-specific knowledge.