Establishing an accurate objective evaluation metric of image sharpness is crucial for image analysis, recognition and quality measurement. In this review, we highlight recent advances in no-reference image quality assessment research, divide the reported algorithms into four groups (spatial domain-based methods, spectral domain-based methods, learning-based methods and combination methods) and outline the advantages and disadvantages of each method group. Furthermore, we conduct a brief bibliometric study with which to provide an overview of the current trends from 2013 to 2021 and compare the performance of representative algorithms on public datasets. Finally, we describe the shortcomings and future challenges in the current studies.