The analytical and numerical modelling of the behaviour of magnetohydrodynamic (MHD) waves in various magnetic geometries is a constantly evolving, active area of research within the field of solar magneto-seismology. Here, we present our findings on MHD wave propagation and instabilities in a family of asymmetric Cartesian waveguide models. Thanks to the introduction of various sources of asymmetry (background density, magnetic field or flow speed), this generalisation of classical (symmetric) slab geometries allows us to refine our modelling of several important features in the richly structured solar atmosphere. Including background asymmetry in these configurations influences the phase speeds and cut-off frequencies of the eigenmodes, and, in the case of flow asymmetry, it can also change the threshold for the onset of the Kelvin-Helmholtz instability. Furthermore, the asymmetric nature of the models allows us to develop solar magneto-seismologic tools and provide efficient methods for obtaining further information about the solar plasma from current and future high-resolution observations of multi-layered waveguides (such as e.g. magnetic bright points or light walls).