Theoretical quantum advantage is well-established in centralized computing, where computation is performed on a single computer. However, its potential in distributed computing is less understood. In this talk, we consider the LOCAL model of computation (Linial 1987), a model of synchronous distributed computation where the complexity measure is the number of communication rounds needed to solve a problem, with no constraints on communication bandwidth or local computation capabilities. The classical LOCAL model is well-studied, especially regarding Locally Checkable Labeling (LCL) problems (Naor and Stockmeyer 1993), which include problems like graph coloring, finding maximal independent sets, etc. Yet, we still do not fully understand how much quantum computers and quantum communication can speed up computation in this setting. Currently, no tools specific to quantum-LOCAL exist to address this question. Nevertheless, recent work has used causality and independence arguments to “sandwich” the quantum-LOCAL model between classical LOCAL and hypothetical super-quantum models. These investigations draw on tools from probability theory, descriptive combinatorics, and topology. This talk serves as a brief introduction to the topic, highlighting key limitations---problems where quantum advantage is impossible---and settings where, instead, quantum advantage can, in principle, be possible.