Giant radio galaxies are believed to be formed from relativistic jets of matter and energy, emanating from the central regions of active galactic nuclei.  Synchrotron radiation, often polarised, from the radio jets and lobes of these objects will be studied with LOFAR.  The low-energy electrons responsible for the low-frequency emission can propagate large distances from their origins in the central core or lobe hotspots, and large radio cocoons are expected to surround many objects.  Using high angular resolution observations with the full international LOFAR array should help us to learn more about the low-energy electron population in these objects, and hopefully to better understand the acceleration mechanisms which produce the relativistic electrons responsible for synchrotron emission. The high degrees of polarisation of giant radio galaxies makes them ideal polarisation calibrators for the observation of weaker sources.