Although it has many positive effects, soil structure may adversely affect the filtering function of the vadose zone that protects natural water resources from various sources of pollution. Physically based models have been developed to analyze the impacts of preferential water flow (PF) and physical non-equilibrium (PNE) solute transport on soil and water resources. This review compiles results published over the past decade on the application of such models for simulating PF and PNE non-reactive tracer transport for scales ranging from the soil column to the catchment area. Recent progress has been made in characterizing the hydraulically relevant soil structures, dynamic flow conditions, inverse parameter and uncertainty estimations, independent model parameterizations, stochastic descriptions of soil heterogeneity, and 2D or 3D extensions of PNE models. Two-region models are most widely used across all scales; as a stand-alone approach to be used up to the field scale, or as a component of distributed, larger scale models. Studies at all scales suggest that inverse identification of parameters related to PF is generally not possible based on a hydrograph alone. Information on flux-averaged and spatially distributed local resident concentrations is jointly required for quantifying PNE transport. At the column and soil profile scale, model predictions of PF are becoming increasingly realistic through the implementation of the 3D soil structure as derived from hydrogeophysical and tracer techniques. At the field scale, integrating effects of the soil structure and its spatial variability has been attempted by combining 1D PNE approaches with stochastic parameter sampling. At the catchment area scale, the scarcity of data makes validation of PF related model components a task yet to be accomplished. The quest for easily measurable proxy variables, as 'the missing link' between soil structure and model parameters, continues in order to improve the practical predictive capability of PF-PNE models. A follow-up paper complementing this manuscript reviews model applications involving non-equilibrium transport of pesticides, as representatives of reactive solutes.