Sensitive, high-resolution radio continuum observations are uncovering details of the complex interaction between kpc-scale AGN jets and their environments. I will present theoretical results from a suite of analytical and numerical models of AGN jets, designed to inform interpretation of radio continuum observations. I will show how analytical jet models provide insights into poorly constrained physical processes, including mechanisms responsible for jet intermittency, and modes of AGN feedback in galaxies and clusters. I will then introduce the CosmoDRAGoN simulations, a large suite of simulated AGN jets in cosmological environments. CosmoDRAGoN uses 3D relativistic hydrodynamic simulations to describe jet dynamics, while synchrotron emissivity is calculated in post-processing using an analytical model which fully accounts for the relevant loss processes. The CosmoDRAGoN simulation data, including synthetic radio images, are being made available to the community via a web app. I will show how these simulations can be used to probe galaxy and cluster-scale environments, and robustly classify radio galaxies in different evolutionary stages. I will conclude with a possible formation mechanism for Odd Radio Circles (ORCs), as radio galaxy remnants revived by the passage of a shock.