We review several infiltration phenomena and modeling approaches for unsaturated porous media. First, we present a recent extension of the piston flow model of Green & Ampt, called Moving Multi-Front (MMF), which propagates vertically a discrete number of “fronts” or pressure iso-values. Secondly, based on the general Richards PDE governing variably saturated flow, we analyze several infiltration phenomena like capillary barrier phenomena due to heterogeneities in 1D (vertically discontinuous water contents) and in 2D (perched water over a clay lens in vertical cross-section). Thirdly, we present previously unpublished modeling and analyses of the 2D/3D dynamics of moisture plumes and ponded zones during localized infiltration from point sources and line sources (drip irrigation)