The exponential growth of massive data streams is everywhere, and has been attracting increasing interest. In addition to size, the complexity is certainly an important issue. To handle this kind of datasets, of particular importance is an adaptive model, as well as innovative acquisition of intrinsic features/structure hidden in the massive data-sets. In this talk, I will discuss how to apply the knowledge from differential geometry to model and analyze massive datasets in different fields. In particular, I will discuss algorithms like graph connection Laplacian and vector diffusion maps, and their theoretical justification based on the spectral geometry. I will also discuss at least one of the following applications: cryo-electron microscope, phase retrieval, vector nonlocal mean and F wave analysis.