In order to facilitate the understanding of the current research efforts and directions, this article first introduces the anomalous/problematic features of magnesium, and presents the recent approach of stacking fault energy (SFE)-based alloying element selection to lessen or eliminate these problem. SFE computations via ab initio techniques necessitate an understanding of the free electron density distribution around atoms in a solid solution. Therefore, the assessment of the role of atoms by also considering the possibility of short range order (SRO) formation rather than a random solid solution has been revisited. Two possible types of SRO have been indicated. The relevant electronic interactions between the host Mg and the alloying element atoms are more clearly incorporated in, a generally less known model, by Miedema’s based on atomic level thermodynamics rather than in Hume-Rothery rules. This more successful approach has also been addressed here. An evaluation founded on these premises, introducing the relatively more recent magnesium alloy systems, has been given in terms of their achievements towards healing the problematic features of magnesium alloys. The spectrum of alloy systems discussed ranges from doping of magnesium to dilute alloy systems, and to some rich alloy systems that offer remarkable properties. Among the first category, an unorthodox addition, doping with oxygen, and its implications has been presented. The dilute alloy systems and their compositional design based on short range order (SRO) and SFE together with their potentials have been reviewed. Among the rich alloy compositions, the most interesting precipitate systems, i.e. the ones involving order and intermetallic formations, long period stacking order (LPSO) phases, and quasi-crystals have been discussed. Among all the alloying elements, one that deserves particular attention, with its implications such as being economical, offering environmentally friendly magnesium metallurgy, as well as remedial effects on the shortcomings of engineering properties, calcium and a closely related issue of CaO addition, have been scrutinized. This article also makes an attempt to point out the future directions throughout the text, whenever possible.