Reliable assessment of static and dynamic petrophysical properties of hydrocarbon-bearing reservoirs is critical for estimating hydrocarbon reserves, identifying good production zones, and planning hydro-fracturing jobs. Conventional well-log interpretation methods are adequate to estimate static petrophysical properties (i.e., porosity and water saturation) in formations consisting of thick beds. However, they are not as reliable when estimating dynamic petrophysical properties such as absolute permeability, movable hydrocarbon saturation, and saturation-dependent capillary pressure and relative permeability. Additionally, conventional well-log interpretation methods do not take into account shoulder-bed effects, radial distribution of fluid saturations due to mud-filtrate invasion, and differences in the volume of investigation of the various measurements involved in the calculations. This dissertation introduces new quantitative methods for petrophysical and compositional evaluation of water- and hydrocarbon-bearing formations based on the combined numerical simulation and nonlinear joint inversion of conventional well logs. Specific interpretation problems considered are those associated with (a) complex mineral compositions, (b) mud-filtrate invasion, and (c) shoulder-bed effects. Conventional well logs considered in the study include density, photoelectric factor (PEF), neutron porosity, gamma-ray (GR), and electrical resistivity. Depending on the application, estimations yield static petrophysical properties, dynamic petrophysical properties, and volumetric/weight concentrations of mineral constituents. Assessment of total organic carbon (TOC) is also possible in the case of hydrocarbon-bearing shale. Interpretation methods introduced in this dissertation start with the detection of bed boundaries and population of multi-layer petrophysical properties with conventional petrophysical interpretation results or core/X-Ray Diffraction (XRD) data. Differences between well logs and their numerical simulations are minimized to estimate final layer-by-layer formation properties. In doing so, the interpretation explicitly takes into account (a) differences in the volume of investigation of the various well logs involved, (b) the process of mud-filtrate invasion, and (c) the assumed rock-physics model. Synthetic examples verify the accuracy and reliability of the introduced interpretation methods and quantify the uncertainty of estimated properties due to noisy data and incorrect bed boundaries. Several field examples describe the successful application of the methods on (a) the assessment of residual hydrocarbon saturation in a tight-gas sand formation invaded with water-base mud (WBM) and a hydrocarbon-bearing siliciclastic formation invaded with oil-base mud (OBM), (b) estimation of dynamic petrophysical properties of water-bearing sands invaded with OBM, (c) estimation of porosity and volumetric concentrations of mineral and fluid constituents in carbonate formations, and (d) estimation of TOC, total porosity, total water saturation, and volumetric concentrations of mineral constituents in the Haynesville shale-gas formation. Comparison of results against those obtained with conventional petrophysical interpretation methods, commercial multi-mineral solvers, and core/XRD data confirm the advantages and flexibility of the new interpretation techniques introduced in this dissertation for the quantification of petrophysical and compositional properties in a variety of rock formations.