Depth maps produced by LiDAR based approaches are sparse. Even high-end LiDAR sensors produce highly sparse depth maps, which are also noisy around the object boundaries. Depth completion is the task of generating a dense depth map from a sparse depth map. While the traditional approaches focus on directly completing this sparsity from the sparse depth maps, modern techniques use RGB images as a guidance tool to resolve this problem. Whilst many others rely on affinity matrices for depth completion. Based on these approaches, we have sub-divided the literature into two major categories; traditional approaches and backbone-based approaches. The latter is further sub-divided into two-branch, and spatial propagation approaches. The two-branch approaches still have a sub-category named guided-kernel approaches. In this paper, for the first time ever we present a comprehensive survey of depth completion methods. We present a novel taxonomy of depth completion approaches, review and detail different state-of-the art techniques within each category for depth completion of LiDAR data, and provide quantitative results for the approaches on KITTI and NYUv2 depth completion benchmark datasets.