In this lecture I examined the relationships between and functions of engineers’ drawings and models with focus on the development of nineteenth century mechanical drawings in the context of British industrialization. I discussed how distinctive styles of engineering drawing as seen in the work of various celebrated figures such as John Smeaton or James Watt emerged within the period of ‘industrial enlightenment’ around 1800. Here engineers developed various spheres of operation: in the two-dimensional world of paper where they presented ‘engineering’ in texts and images, as well as in the three-dimensional world of material structures, professional rivalry, and factory organization. When considering the interaction of drawings as models we differentiate two areas: first, thinking about drawings as models, second considering drawing in contrast to 3-D models. As drawings are static and often bloodless well-composed visual statements made in a measured way they obscure or gloss over some difficult aspects of engineering enquiry—because engineers by definition work with intractable and hopelessly mixed up assemblages of elements and materials. Between drawings and 3-D models some enormous gulfs open up. For example, in James Watt’s elegant drawings his condensing steam engines. In actuality, and as we can see in the Hunterian Museum collection, he laboured over a scruffy little contraption constructed in the most ad hoc manner trying to get the most efficient ‘perfect engine’. To close, I reflect on the performative and disciplinary aspects of drawing as model-making: Engineers made drawings, models and structures of various kinds, but their drawing and model making was part of their self-image and indeed their self-production—where the body disciplines of drawing and making shaped their cognitive styles.