Al-Mg-Cu alloys having Mg:Cu mass ratios >1 can be considered as a new subclass of the classical AA5xxx alloys. The development of this new subclass is driven by the desire to combine the excellent formability of the AA5xxx alloys with the advantages of precipitation hardening. During aging, the present alloys show a characteristic two stage hardening response. The precise hardening mechanisms are not yet completely understood and have been actively debated in recent literature. The present paper will start with a short review of some hot deformation problems (and solutions) that can arise when the AA5xxx series are alloyed with Cu. Further, the main mechanical properties of some of these alloys will be compared with the Cu-free variants. The influence of various parameters like solid solution treatment, quenching rate and pre-strain on the ageing response will be discussed. A short review of our current understanding of the precipitation mechanisms-in particular of the initial stage of hardening will be presented. Earlier results based on various techniques like HRTEM, APFIM and PAS will be confronted with some new results obtained by calorimetry.