In this talk, I will discuss the use of diffusion maps for dimensional reduction and approximation of the generator of Langevin dynamics from simulation data. I will consider both global and local perspectives on diffusion maps, based on whether or not the data distribution has been fully explored.  In the first case, diffusion maps are used to identify the metastable sets and to approximate the corresponding committor functions describing transitions between them. I will also discuss the use of diffusion maps within the metastable sets, formalising the locality via the concept of the quasi-stationary distribution and justifying the convergence of diffusion maps within a local equilibrium.  I will demonstrate both approaches on simple toy-models and higher dimensional molecular dynamics problems, providing technical details about the practical implementation.