Microscopy image enhancement plays a pivotal role in understanding the details of biological cells and materials at microscopic scales. In recent years, there has been a significant rise in the advancement of microscopy image enhancement, specifically with the help of deep learning methods. This survey paper aims to provide a snapshot of this rapidly growing state-of-the-art method, focusing on its evolution, applications, challenges, and future directions. The core discussions take place around the key domains of microscopy image enhancement of super-resolution, reconstruction, and denoising, with each domain explored in terms of its current trends and their practical utility of deep learning.