This paper provides a comprehensive review of deep learning-based single image super-resolution (SISR) methods, categorizing them into two main aspects: efficient neural network architectures and effective optimization objectives. The authors discuss the limitations of baseline methods and present recent advancements that address these limitations. They highlight the importance of combining deep learning with domain knowledge to achieve successful SISR. The paper also reviews various deep architectures, such as SRCNN, VDSR, DRCN, SRResNet, EDSR, and others, detailing their contributions and improvements. Additionally, it explores optimization objectives beyond the traditional mean squared error (MSE), including non-Gaussian additive noises and perceptual loss functions. The paper concludes with a discussion on current challenges and future trends in SISR, emphasizing the need for more sophisticated models that can handle complex degradation scenarios and unknown degradation kernels.This paper provides a comprehensive review of deep learning-based single image super-resolution (SISR) methods, categorizing them into two main aspects: efficient neural network architectures and effective optimization objectives. The authors discuss the limitations of baseline methods and present recent advancements that address these limitations. They highlight the importance of combining deep learning with domain knowledge to achieve successful SISR. The paper also reviews various deep architectures, such as SRCNN, VDSR, DRCN, SRResNet, EDSR, and others, detailing their contributions and improvements. Additionally, it explores optimization objectives beyond the traditional mean squared error (MSE), including non-Gaussian additive noises and perceptual loss functions. The paper concludes with a discussion on current challenges and future trends in SISR, emphasizing the need for more sophisticated models that can handle complex degradation scenarios and unknown degradation kernels.