This monograph aims to provide a state-of-the-art theory and the application of dynamic and transient infinite elements for simulating the far fields of infinite domains involved in many of scientific and engineering problems, based on the author’s own work during the last two decades. While the theoretical aspects of either dynamic infinite elements or transient infinite elements are systematically presented, the related application examples are immediately followed to illustrate the usefulness and applicability of these infinite elements for simulating a wide range of dynamic and transient problems involving infinite domains. To broaden the readership of this monograph, common mathematical notations are used to derive the formulations of both dynamic and transient infinite elements. This enables this monograph to be used either as a useful textbook for postgraduate students or as a valuable reference book for computational geoscientists, geotechnical engineers, civil engineers, geoscientists and applied mathematicians.