The Smoothed Particle Hydrodynamics (SPH) method development is rapidly expanding, with the majority of applications focused on geometrically complex free-surface/interface flow, potentially involving multi-physics. This particle method based on a mollification by convolution to evaluate the differential space operators on a scattered set of calculation points representing macroscopic fluid elements, raises theoretical and numerical issues mainly linked to its meshless and Lagrangian features which are rather unusual in hydrodynamics numerical modeling. Current progress on its theoretical and numerical background will be examined and insights will be given regarding its applicability to complex free-surface problems.