Reduced order modeling is a powerful tool for approximating the solution to parametric / random partial differential equations (PDEs). Classical approaches are formulated for PDEs on Hilbert spaces and involve one single linear space which accurately approximate the set of PDE solutions. This linear space is then used to build an efficient solver for the so-called parameter-to-solution map. However, such approach is not suitable for problems with slowly decaying Kolmogorov n-width, such as convection-dominated problems, as they would require using a linear space of high dimension. For such problems, nonlinear reduced models present an attractive alternative. In a so-called library approximation, the idea is to replace the single linear space by a collection of affine spaces of small dimension and then use, for any given parameter, the appropriate space in the library. In this presentation, we introduce library-based reduced models which can also be formulated on general metric spaces. To build the spaces of the library, we rely on greedy algorithms involving different splitting strategies leading to a hierarchical tree-based representation. We discuss theoretical properties of the algorithms, and illustrate their performances on several numerical examples.