Persistent homology is an effective method to compute topological features with different scales. It captures the birth and death time from a nested sequence of simplicial complexes, and employs the life span of a topological feature to measure its geometric scale and significance. The extraction and application of topological features play an important role in geometric design, spawning some studies on geometric design based on persistent homology. In this paper, we introduced the application studies in two aspects, i.e., the feature extraction of persistent homology and the persistent homology-based modeling and optimization. In the feature extraction of persistent homology, we introduced various methods for topological feature extraction from point clouds and triangular meshes, respectively. Meanwhile, the pipeline for applying topological features to some geometric design problems was summarized. In the persistent homology-based modeling and optimization, we reviewed the simplicial complex reconstruction methods based on topology transform, topology-aware surface reconstruction methods, and topological denoising and optimization based on persistent homology.