Recent studies show significant advances in improving the mechanical properties of magnesium and its alloys. While many papers deal with different alloy compositions, it is apparent that grain size plays a key role in the mechanical behavior of these materials. The ability to produce samples with very fine grain sizes leads to observations of high strength and/or high elongations. There are recent reports of exceptional elongations of over 100% in pure magnesium and a few alloys. These recent findings are critically reviewed in the present study. The experimental data from over 300 papers are collected, and trends between flow stress, elongation, strain rate sensitivity, and grain size are identified. The role of alloy content is examined. The data clearly shows a transition in the flow stress vs. grain size relationship which is attributed to a change in deformation mechanism from twinning controlled in coarse grained to slip controlled in fine and ultrafine grained samples. The slip controlled deformation agrees with the model of grain boundary sliding, which has shown good agreement with multiple metallic materials. It is shown that the elongations display a maximum in the grain size range in which there is a transition in the deformation mechanism. Three strategies are described for achieving high strength, high ductility, and good strength-ductility combination.