Gamma-ray bursts (GRBs) are some of the most extreme events in the Universe. As well as providing a natural laboratory for investigating fundamental physical processes, they might trace the cosmic star formation rate up to extreme redshifts and probe the composition of the intergalactic medium over most of the Universes history. Radio observations of GRBs play a key part in determining their physical properties, but currently they are largely limited to follow-up observations of $gamma$-ray-detected objects. The SKA will significantly increase our ability to study GRB afterglows, following up several hundred objects in the high frequency bands already in the early science implementation of the telescope. SKA1-MID Bands 4 (4 GHz) and 5 (9.2 GHz) will be particularly suited to the detection of these transient phenomena. The SKA will trace the peak of the emission, sampling the thick-to-thin transition of the evolving spectrum, and follow-up the afterglow down to the time the ejecta slow down to non-relativistic speeds. The full SKA will be able to observe the afterglows across the non-relativistic transition, for ~25% of the whole GRB population. This will allow us to get a significant insight into the true energy budget of GRBs, probe their surrounding density profile, and the shock microphysics. The SKA will also be able to routinely detect the elusive orphan afterglow emission, from the population of GRBs whose jets are not pointed towards the Earth. We expect that a deep all-sky survey such as SKA1-SUR will see around 300 orphan afterglows every week. We predict these detection to be >1000 when the full SKA telescope will be operational.