Nuclear Magnetic Resonance (NMR) well logging is finding wide use in formation evaluation. In most cases, it is adequate to use default parameters and interpretation methods to get formation properties. In this work, we will investigate three exceptional cases: The departure of the hydrogen index ( HI) of live crude oils from unity due to high solution gas:oil ratio; The wettability alteration from water-wet condition to some degree of mixed wettability for sandstones; Significant diffusion effect on NMR spin-spin relaxation time (T2) measurements due to internal field gradients. A new correlation is proposed to express HI as a function of density and hydrogen:carbon ratio. The HI of live crude oils can be calculated from PVT data and ambient measurements. Wettability alteration is interpreted for sandstones from NMR analysis. Bentheim and Berea were water-wet with refined oil but became mixed-wet with SMY crude oil and brine at Swir after aging. North Burbank sandstones were even mixed-wet with refined oil due to the pore lining chlorite clay flakes. NMR wettability analysis is consistent with other quantitative wettability alteration indicators. Strong internal field gradients are measured for both chlorite-coated North Burbank sandstones and chlorite slurries. The distributions of internal field gradients are analytically solved through potential theory. High gradients are concentrated around the tips of the clay flakes. Mean gradient values from analytical solutions using a clay width of 0.2 mum are close to the experimental results. The combined effects of diffusion, constant gradient, and restricted 1-D geometry on Carr-Purcell_Meiboom_Gill (CPMG) measurement are evaluated numerically. The parameter space that defines the relaxation process is reduced to only two dimensionless groups: D* and tau*. The hypothesis that the dimensionless normalized magnetization relaxes as a single exponential with a constant dimensionless relaxation time T*2 is justified for most regions of the parameter space. The location of the boundaries between different relaxation regimes defined in the analytical analysis is challenged by the numerical results. After adjustment of boundaries, numerical simulation results and analytical solutions match each other for every relaxation regime except for near the boundaries. A procedure to estimate fluid diffusivity and system length is illustrated.