  Cosmic rays with energies up to $10^{11}\,\mathrm{GeV}$ enter the atmosphere
and produce showers of secondary particles. Inside these showers muons with
high transverse momentum ($p_\mathrm{T} \gtrsim 2\,\mathrm{GeV}$) are produced
from the decay of heavy hadrons, or from high $p_\mathrm{T}$ pions and kaons
very early in the shower development. These isolated muons can have large
transverse separations from the shower core up to several hundred meters,
together with the muon bundle forming a double or triple track signature in
IceCube. The separation from the core is a measure of the transverse momentum
of the muon's parent particle. Assuming the validity of perturbative quantum
chromodynamics (pQCD) the muon lateral distribution depends on the composition
of the incident nuclei, thus the composition of high energy cosmic rays can be
determined from muon separation measurements. Vice versa these muons can help
to understand uncertainties due to phenomenological models as well as test pQCD
predictions of high energy interactions involving heavy nuclei. After
introducing the physics scenario of high $p_\mathrm{T}$ muons in
kilometer-scale neutrino telescopes we will review results from IceCube in its
59-string configuration as starting point and discuss recent studies on
composition using laterally separated muons in the final detector
configuration.
