Although radio-quiet quasars (RQQs), which constitute the majority of optically-identified quasar samples, are by no means radio silent the properties of their radio emission are only poorly understood. We present the results of a multi-frequency VLA study of 27 low-redshift RQQs. In general, we find that the properties of the radio sources in RQQs are consistent with them being weak, small-scale (~1 kpc) jets similar to those observed in nearby Seyfert galaxies. We conclude that a significant fraction of the radio emission in RQQs is directly associated with the central engine and is not a result of stellar processes in the surrounding galaxy. There appears to be no difference between the radio properties of RQQs in elliptical and disc galaxies, implying that the relationship between the host galaxy and the `radio loudness of the active nucleus is not straightforward.