Muons interact with the electromagnetic and weak interaction. They are ~200 times heavier than the electrons. In this link the behavior of charged particles with matter is discussed. Generally heavy charged particles pass through matter with electromagnetic interactions that ionize the medium. Electrons in addition lose a lot of energy to bremsstrahlung due to their small mass.
Thus electrons will be stopped in the electromagnetic calorimeters designed so that gamma rays and electrons will be stopped. Hadrons, protons and neutrons, will be stopped in the hadronic calorimeter because they are designed to take advantage oof their strong interactions with the nuclei. Muons interact only weakly, and thus leave just a track footprint in the calorimeters. They need a lot more matter so that they can be detected, by elimination of the other particles.
Here is an image of the CMS detector:
The above illustration is a slice of the CMS detector from the collision point to the perimeter as shown in the lower left hand corner. The various colored curved lines represent paths that a particle might take, for example, the red line represents an electron.
Muons are the blue line. Any charged particle that does not interact in the calorimeters is identified as a muon, leaving the detector without interacting except by ionisation. The large return yoke necessary for the magnetic field of the detector is taken advantage of to determine that really this charged particle is a non interacting one, by interspersing muon tracking detectors so that the track can be fitted also for momentum determination.