The construction of viable and physically-realistic interstellar dust models is only possible if the constraints imposed by laboratory data on interstellar dust analogue materials are respected and used within a meaningful theoretical framework. These “physical” dust models can then be directly compared to observations without the need for any tuning to fit the observations. Such models will generally fail to achieve the excellent fits to observations that “empirical” models are able to achieve. However, the physically-realistic approach will necessarily lead to a deeper insight and a fuller understanding of the nature and evolution of interstellar dust. The THEMIS modelling approach, based on (hydrogenated) amorphous carbons and amorphous silicates with metallic Fe and/or FeS nano-inclusions appears to be a promising move in this direction.