Optical microscopy has emerged as a key driver of fundamental research since it provides the ability to probe into imperceptible structures in the biomedical world. For the detailed investigation of samples, a high-resolution image with enhanced contrast and minimal damage is preferred. To achieve this, an automated image analysis method is preferable over manual analysis in terms of both speed of acquisition and reduced error accumulation. In this regard, deep learning (DL)-based image processing can be highly beneficial. The review summarises and critiques the use of DL in image processing for the data collected using various optical microscopic techniques. In tandem with optical microscopy, DL has already found applications in various problems related to image classification and segmentation. It has also performed well in enhancing image resolution in smartphone-based microscopy, which in turn enablse crucial medical assistance in remote places.