Ultrasound Localization Microscopy (ULM) is a novel super-resolution imaging technique that can image the vasculature in vivo at depth with resolution far beyond the conventional limit of diffraction. By relying on the localization and tracking of clinically approved microbubbles injected in the blood stream, ULM can provide not only anatomical visualization but also hemodynamic quantification of the microvasculature of different tissues. Various deep-learning approaches have been proposed to address challenges in ULM including denoising, improving microbubble localization, estimating blood flow velocity or performing aberration correction. Proposed deep learning methods often outperform their conventional counterparts by improving image quality and reducing processing time. In addition, their robustness to high concentrations of microbubbles can lead to reduced acquisition times in ULM, addressing a major hindrance to ULM clinical application. Herein, we propose a comprehensive review of the diversity of deep learning applications in ULM focusing on approaches assuming a sparse microbubbles distribution. We first provide an overview of how existing studies vary in the constitution of their datasets or in the tasks targeted by deep learning model. We also take a deeper look into the numerous approaches that have been proposed to improve the localization of microbubbles since they differ highly in their formulation of the optimization problem, their evaluation, or their network architectures. We finally discuss the current limitations and challenges of these methods, as well as the promises and potential of deep learning for ULM in the future.