Semiconductor drift-diffusion models are a standard tool to describe how charge carriers move inside electronic devices. Although they are based on the same physical principles, these models can be written in several equivalent ways, for instance, in terms of carrier densities, quasi-Fermi potentials, or Slotboom variables. At a formal level, these formulations describe the same problem, but they differ significantly in their mathematical structure, with important consequences for both analysis and computation. In this talk, we explore how the choice of variables affects the structure of the drift-diffusion system and the methods used to study it, showing in particular how different formulations lead to distinct approaches for proving existence of solutions and naturally extend to more complex settings arising in current research, such as coupled circuit–device models, interactions with optical fields in laser devices, and the impact of different simulation techniques.