A novel nonequilibrium molecular dynamics (NEMD) method introduced in 1994 and its recent application to investigations of the transport properties of gases and dense fluids within strongly inhomogeneous pore structures are reviewed. In this technique molecular simulations are conducted under realistic nonequilibrium (experimental) conditions thus enabling direct insight into the underlying microscopic processes taking place during transport within pores. The case studies reviewed in this paper establish the versatility and scope of the NEMD technique and also demonstrate its significant advantages over prior molecular simulation procedures as a tool to assist in the design and tailoring of novel nanopore systems.