In this talk, we will introduce our recently proposed persistent models for molecular representation and featurization. In our persistent models, molecular interactions and structures are characterized by various topological objects, including hypergraph, Dowker complex, Neighborhood complex, Hom-complex. By considering a filtration process of the representations, various persistent functions can be constructed from the mathematical invariants of the representations through the filtration process, like the persistent homology and persistent spectral. These persistent functions are used as molecular descriptors for the machine learning models. The state-of-art results can be obtained by these persistent function based machine learning models.