Since all structures are founded on the earth's crust, there is interaction between these systems. The behaviour of one system influences the behaviour of the other and vice-versa. In many situations this interaction affects the structural behaviour significantly and has to be considered in the simulations. However, this interaction is usually neglected and rigid foundations are assumed. Therefore, to ensure reliable and accurate simulation models, the interaction between structure and surrounding medium (e.g., soil and/or fluid) must not be neglected, which implies that the time response of both subsystems must be evaluated simultaneously. It is also important to consider the external actions which vary in time (e.g., earthquake and wind loading). In order to carry out this task, the whole system may be treated as a coupled system (or a multi-region problem), by means of appropriate techniques. Numerical solutions for the aforementioned problems call for the use of discrete techniques such as the Finite Element Method (FEM) or the Boundary Element Method (BEM). These methods are respectively based on domain or boundary discretization, and the governing equations are written as a system of algebraic equations with respect to time and space. The motivation for the thesis is therefore to develop efficient, accurate and robust numerical simulations methods based on the coupling of FEM/BEM for dynamic multi-region problems, with special emphasis on the BEM. The thesis consists of seven chapters. Chapter 1 contains the introduction. Selected boundary value problems, such as those governed by Laplace equation, scalar wave equation and Navier's equation, are reviewed in Chapter 2 in order to describe the boundary element formulations used to treat such problems, in terms of governing equations, boundary integral equation and discretization. Chapter 3 introduces the interface stiffness matrix approach for modelling of static multi-region problems, on which the dynamic formulations are based. This approach is derived here using variational basis, where a coupling strategy is formulated by considering only interface unknowns (partially coupled problems). The formulation proposed in Chapter 3 is based on the ideas presented by Aour et al. (2007), who introduced a coupled FEM/BEM approach via total potential energy minimization, for fully coupled problems. The authors believe that this is the first time a variational basis is used to formulate this type of partially coupled problems, by setting up the system of equations for coupling only unknowns at the interfaces. In addition, the multi-region problems are also formulated based on classical Lagrange multipliers to derive a novel weak coupling approach. In Chapter 4, an introduction to the Duhamel integral equation is presented. Then, the proposed formulations for transient dynamic multi-region problems are introduced. The first approach combines the ideas for the coupling strategy presented in Chapter 3 with the concept of Duhamel integrals. This approach is applied to both solid regions (structure and soil), as well as to the acoustic fluid regions. Also, the coupling to finite elements is described and a flow chart for each proposed approach is presented. Finally, to overcome some limitations of the first approach, an alternative approach is introduced. Applications presented in Chapter 5, numerical experiments including both academic examples and problems of technical significance on soil-structure and fluid-structure interaction problems (foundation embedded in a half-space soil; dam-water interaction; seismic simulation in an underground excavation) validate and investigate the accuracy, stability and efficiency of the proposed methodologies. The obtained results are compared with results from the literature. Finally, the conclusions and directions for future work are discussed in Chapter 6.