Continuous data come in many varieties: a time-dependent value is 1D data, whereas a photo can be seen as data whose domain is two-dimensional and whose range is R^3 (we have three color values for each point of the image). There are many standard methods for the analysis, storage, compression, and processing of such data: I would like to mention wavelet analysis, or the JPEG graphics format. These methods are linear and will therefore work only to a limited extent if the data we must handle live in genuinely nonlinear geometries: Examples are the time-dependent position of a rigid body in space, or diffusion tensor images. This presentation will describe some new developments and results in this area.