The long time evolution of initial data consisting of a soliton and a positive or negative step are considered for the Korteweg-de Vries (KdV) equation. The positive/negative step evolves into a rarefaction wave/dispersive shock wave that either transmits or traps the soliton within its interior, the former being identified with a new concept termed hydrodynamic soliton tunneling. In contrast to traditional tunneling involving an external barrier, the extended hydrodynamic state acts as an evolving "barrier" that nonlinearly interacts with the soliton. Two approaches are utilized to analyze the problem. Whitham modulation theory provides a formal asymptotic solution in the form of a simple wave. Inverse scattering theory is used to obtain exact results. The principle findings are the conditions for soliton transmission and the transmitted soliton's amplitude and phase shift due to the hydrodynamic barrier. Reciprocity is observed whereby the soliton interacts in a dual fashion with rarefactions and dispersive shock waves. Trapping is shown to occur when KdV's associated

Schrödinger scattering problem exhibits an embedded eigenvalue. The two approaches are found to agree in their common domains of validity and are further supported by numerical simulations. Generalizations to non-integrable systems are also presented. Finally, experimental observations of this phenomena in the viscous fluid conduit system reveal its practical, physical nature. This work is in collaboration with M. J. Ablowitz, D. V. Anderson, J. Cole, G. A. El, X. Luo, and M. D. Maiden.