Theory of Two-Dimensional Dynamic Infinite Elements for Simulating Wave Propagation Problems in Infinite Media -- Application of Two-Dimensional Dynamic Infinite Elements: Simulation of Dynamic Dam-Water-Foundation Interaction Problems -- Application of Two-Dimensional Dynamic Infinite Elements: Simulation of Wave Scattering Effects under Different Canyon Topographical and Geological Conditions -- Theory of Three-Dimensional Dynamic Infinite Elements for Simulating Wave Propagation Problems in Infinite Media -- Application of Three-Dimensional Dynamic Infinite Elements: Simulation of Dynamic Structure-Foundation Interaction Problems -- Theory of Transient Infinite Elements for Simulating Pore-Fluid Flow and Heat Transfer in Porous Media of Infinite Domains -- Theory and Application of Transient Infinite Elements for Simulating Contaminant Transport Problems in Fractured Porous Media of Infinite Domains. Effective and ef cient modelling of in nite media is important for the production of accurate and useful solutions for many scienti c and engineering problems invo- ing in nite domains (Bettess 1977, 1980; Chow and Smith 1981; Medina and Taylor 1983; Zhang and Zhao 1987; Zhao et al. 1989; Zhao and Valliappan 1993a, b, c, d; Astley 1996, 1998; Yang et al. 1996; Yang and Huang 2001; Yun et al. 2000, 2007; Wang et al. 2006). Some typical examples involving in nite domains are as follows: (1) earthquake wave propagation within the upper crust of the Earth in the elds of geophysics and seismology; (2) dynamic structure-foundation interaction in the elds of geotechnical, civil and dam engineering; and (3) transient pore- uid ow, heat transfer and mass transport within the interior of the Earth in the elds of g- science and geoenvironmental engineering. Although the solid Earth is viewed as a bounded domain at the terrestrial scale, it can be treated as an unbounded domain at the human scale. For instance, in the case of predicting possible property damages caused by an earthquake, only a limited region around the epicentre is of interest because the earthquake wave energy is signi cantly reduced as the distance from the epicentre is increased.