Abstract: Nuclear magnetic resonance is a well-established technique that has found applications in a wide array of different fields such as quantum information processing, molecular structures of proteins, or functional imaging of brain activities. In all these applications, the sample is placed inside a superconducting magnet with a field of high strength and high homogeneity. In contrast, NMR well logging is an implementation of NMR where teh sample is located outside the magnet. This technique enables the evalution of fluids in earth formations many kilometers underground and has been made possible by the development of specialized hardware adapted to the harsh environmental conditions and by novel measurement techniques that probe the diffusion properties of the fluids in the porous media. I will give an overview of the technique of NMR well logging and its commercial relevance, and then discuss various aspects of the underlying Physics. The measurement is complicated by the fact that the spin system is exposed to grossly inhomogeneous magnetic fields. It will be shown that with optimally modulated excitation and refocusing pulses, it is possible to generate a surprisingly robust response that also allows the quantitative determination of multi-dimensional distribution functions of diffusion and relaxation. These distribution functions encode information on the composition and quantity of the fluids occupying the pore space, the geometry of the pore space, and the relative configuration of the various fluid phases within the pore space.