Upscaling is a process which delivers coefficients for a numerical method at a scale much coarser than the (fine) scale at which data is actually available. Solving at a coarse scale may reduce the computational time, perhaps even by orders of magnitude. Upscaling can be cast as both i) a numerical homogenization procedure, and as ii) a parameter identification method. The outcome depends on what quantity is minimized in the upscaling process, what regularization, and what numerical method are used. In the talk(s) we explore both points of view, and focus on linear and nonlinear elliptic PDEs with applications to flow in porous media. In part I we focus on linear problems and introduce the topic and the basic conforming and nonconforming finite element methods. In part II we present our recent results for non-Darcy flow in porous media obtained with Cristiano Garibotti.