Digital elevation model acquisition is the precondition of smart city construction. The airborne LiDAR technology provides a new approach for building the digital elevation model. Accurate ground point cloud filtering is the key to constructing the digital elevation model, so filtering for airborne LiDAR point cloud has always been a research hotspot and difficulty. As the morphological algorithms are simple and efficient, they are the mainstream in the point cloud filtering. To deep understand the algorithms, we summarize existed morphological filtering algorithms at home and abroad, analyze the characteristics, resolved problems and unresolved problems of various filtering methods, and present the prospect of the algorithms based on the unresolved problems.