We present an analytically solvable minimal model for the relaxation of low-frequency magnons in magnetic insulators arising from magnon–phonon and magnon–magnon interactions. The model establishes a direct connection between microscopic relaxation processes and Gilbert damping, and reveals how magnon decay evolves from bulk systems to the monolayer limit. We find that magnon–phonon coupling produces Gilbert damping of comparable magnitude in three- and two-dimensional magnets, with qualitative differences between flexural phonons in free-standing monolayers and three-dimensional phonons in substrate-supported layers. By contrast, non-Gilbert damping due to four-magnon scattering is strongly enhanced in two dimensions, where it becomes independent of spin–orbit coupling. To benchmark the model against real materials, we introduce a numerical approach for computing magnon damping from ab initio–derived spin Hamiltonians. We demonstrate that the central conclusions of the model remain valid for magnons in bulk YIG and several van der Waals magnetic insulators: CrSBr, CrI3 and CrPS4.