Engineering academic units might engage with social media for a range of purposes including for general communication with students, staff, alumni, other important stakeholders and the wider community at large; for student recruitment and for marketing and promotion more generally. This paper presents an investigation into the use of Twitter by six engineering academic units internationally, using publicly available Twitter data over an 18-month period for analysis and visualization, to characterize the engagement by engineering academic units with one popular social media tool. Widely varying levels of activity were observed, from essentially undirected "Megaphone" Tweeting, through to sustained and complex interactions with multiple external accounts. This work provides insights into how engineering academic units are using Twitter and how they might more effectively use the platform to achieve their individual objectives for institutional social media communications and marketing, and offers a methodology for future research.