The challenges of low-frequency radio polarimetry: lessons from the Murchison Widefield Array

We present techniques developed to calibrate and correct Murchison Widefield Array (MWA) low frequency (72-300 MHz) radio observations for polarimetry. The extremely wide field-of-view, excellent instantaneous (u, v)-coverage and sensitivity to degree-scale structure that the MWA provides enable instrumental calibration, removal of instrumental artefacts, and correction for ionospheric Faraday rotation through imaging techniques. With the demonstrated polarimetric capabilities of the MWA, we discuss future directions for polarimetric science at low frequencies to answer outstanding questions relating to polarised source counts, source depolarisation, pulsar science, low-mass stars, exoplanets, the nature of the interstellar and intergalactic media, and the solar environment.