Biological super-resolution microscopy is a new generation of imaging techniques that overcome the ~200 nm diffraction limit of conventional light microscopy in spatial resolution. By providing novel spatial or spatiotemporal information on biological processes at nanometer resolution with molecular specificity, it plays an increasingly important role in biomedical sciences. However, its technical constraints also require trade-offs to balance its spatial resolution, temporal resolution, and light exposure of samples. Recently, deep learning has achieved breakthrough performance in many image processing and computer vision tasks. It has also shown great promise in pushing the performance envelope of biological super-resolution microscopy. In this brief review, we survey recent advances in using deep learning to enhance the performance of biological super-resolution microscopy, focusing primarily on computational reconstruction of super-resolution images. Related key technical challenges are discussed. Despite the challenges, deep learning is expected to play an important role in the development of biological super-resolution microscopy. We conclude with an outlook into the future of this new research area.