Abstract: The model of random interlacements was introduced in 2007 by A.-S. Sznitman, motivated by questions about the disconnection of discrete cylinders or tori by the trace of simple random walk. Since then, it has gained popularity among probabilists due to its percolative properties and also because of its connections to the free field. Random interlacements on transient graphs can be constructed as a Poisson point process of doubly infinite trajectories. After reviewing this model, we will focus on the rare event that these trajectories disconnect a macroscopic body from infinity, in the strongly percolative regime. We will ask the following question: What is the most efficient way for random interlacements to enforce such disconnection? In other words, how do the trajectories of random interlacements look like conditionally on disconnection?