In this paper, the travelling-wave thermoacoustic engine (TAE) and its application for recovery of waste heat from automotive exhaust systems is investigated. The aim is to give some insight into the potential, but also limitations of the technique for practical applications. This includes packaging, physical boundary conditions as heating and cooling available, but also system perspectives as influence of legislative drive cycles and degree of hybridization. First, the travelling-wave TAE is described as a low-order acoustic network in the frequency domain. Models, including non-linear effects, are set up for every component in the network to describe the propagation and dissipation of acoustic waves. For a TAE with looped structure, the continuity of pressure and volumetric velocity is employed to determine the saturation pressure, as well as the stable operating point. These models are validated against experimental data available in the literature [1]. This is an engine designed for high-temperature application, but is well documented and yields a good reference for the models and to further the understanding of the TAE. Next, an optimized design for a system to be adapted to the operating conditions typical for heavy-duty systems is studied and proposed. No actual physical prototype has been built and verified, but the design is based on, and is of the same efficiency, as machines that have been reported in the literature. The proposed design and the original TAE are then used to discuss the practical implementation for heavy- and light-duty vehicles on a system level. To improve the utilization of the available exhaust waste heat, a configuration of system heat exchangers combining a self-circulating loop with multiple TAE modules is preliminarily studied. Further research for this configuration is needed for practical implementation although current simulation results are encouraging.