Only a few of the current supersymmetry theories predict the existence of R-hadrons, since in most of the parameter space all the supersymmetric particles are so separated in mass that their decays are very fast (with the exception of the LSP, which is stable in all the SUSY theories with R-parity).
R-hadrons are possible when a colored (in the sense of QCD) supersymmetric particle (e.g., a gluino or a squark) has a mean lifetime longer than the typical hadronization time scale, and so QCD bound states are formed with ordinary partons (quarks and gluons), in analogy with the ordinary hadrons.
One example of a theory predicting observable R-hadrons is Split SUSY. Its main feature is, in fact, that all the new bosons are at a very high mass scale, and only the new fermions are at the TeV scale, i.e. accessible by the ATLAS and CMS experiments in collisions at LHC. One of such new fermions would be the gluino (spin 1/2, as dictated for the supersymmetric partner of a spin 1 boson, the gluon). The gluino, being colored, can only decay to other colored particles. But R-parity prevents a direct decay to quarks and/or gluons, and on the other hand the only other colored supersymmetric particles are the squarks, that being bosons (spin 0, being the partners of the spin 1/2 quarks) have a much higher mass in Split SUSY.
All this, together, implies that the decay of the gluino can only go through a virtual particle, a high-mass squark. The mean decay time depends on the mass of the intermediate virtual particle, and in this case can be very long. This gives a unique opportunity to observe a SUSY particle directly, in a particle detector, instead of deducing it by reconstructing its decay chain or by the momentum imbalance (as in the case of the LSP).
In the following, for sake of illustration, the R-hadron will be assumed to originate from a gluino created in a collision at LHC, but the observational features are completely general.
Since some of the sub-detectors of a typical high-energy experiment are only sensitive to charged particles, one possible signature is the disappearance of the particle (going from charge +1 or -1 to 0) or vice versa its appearance, while keeping the same trajectory (since most of the momentum is carried by the heaviest component, i.e. the supersymmetric particle inside the R-hadron). Another signature with very little background would come from the complete inversion of the charge (+1 into -1 or vice versa). Almost all tracking detectors at high-energy colliders make use of a magnetic field and are then able to identify the charge of the particle by its curvature; a change of curvature along the trajectory would be recognized unambiguously as a flipper, i.e. a particle whose charge has flipped.
This article incorporates material from the Citizendium article "R-hadron", which is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License but not under the GFDL.