We give an overview of some results we obtained in the last three years about the so-called Interaction Abstract Machine (IAM in the following) and its efficiency in time and space. More specifically, we are interested in checking whether any invariance result in the style of Slot and van Emde Boas is possible for the IAM. Unfortunately, the answer is going to be negative. Still, while the time inefficiency of the IAM is expected, its space inefficiency could be seen as surprising, given, e.g., the well-known results of Schöpp and coauthors on the characterization of logarithmic space computable functions through a construction very closely related to the IAM. We conclude the talk by giving some observations about the IAM’s reversibility properties, which can be seen as partially justifying the results above.