Image super-resolution (SR) is one of the vital image processing methods that improve the resolution of an image in the field of computer vision. In the last two decades, significant progress has been made in the field of super-resolution, especially by utilizing deep learning methods. This survey is an effort to provide a detailed survey of recent progress in single-image super-resolution in the perspective of deep learning while also informing about the initial classical methods used for image super-resolution. The survey classifies the image SR methods into four categories, i.e., classical methods, supervised learning-based methods, unsupervised learning-based methods, and domain-specific SR methods. We also introduce the problem of SR to provide intuition about image quality metrics, available reference datasets, and SR challenges. Deep learning-based approaches of SR are evaluated using a reference dataset. Some of the reviewed state-of-the-art image SR methods include the enhanced deep SR network (EDSR), cycle-in-cycle GAN (CinCGAN), multiscale residual network (MSRN), meta residual dense network (Meta-RDN), recurrent back-projection network (RBPN), second-order attention network (SAN), SR feedback network (SRFBN) and the wavelet-based residual attention network (WRAN). Finally, this survey is concluded with future directions and trends in SR and open problems in SR to be addressed by the researchers.