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Twinning is an important deformation mechanism for magnesium alloys, which has a significant impact on the texture evolution and mechanical properties. Pre-twinning deformation has been considered as an effective method for texture regulation. For each twinning mode, there are six crystallographically equivalent variants. Properly identifying the activated twin and understanding its variant selection criteria are essential for the development of high-performance magnesium alloys. As summarized in this paper, the observed twin variant by the commonly employed electron backscatter diffraction technique can be identified by several approaches, including misorientation analysis, trace analysis and matrix method. Schmid factor analysis was commonly performed to explain the selection of twin variants. To broaden the application scope under complex stress state, a generalized Schmid factor was derived by introducing a stress tensor. The efficiency of Schmid criteria to assess twin variant selection was confirmed to be influenced by the type of the applied stress. To consider the local effect on twin activation, in particular twin-twin transfer and slip-induced twinning, displacement gradient tensor calculation and geometrical compatibility factor analysis have been employed. It was demonstrated that local strain accommodation played a critical role in selecting the variants of cross-boundary twins in magnesium alloys. Assisted with crystal plasticity finite element modeling, the resolved shear stress on twinning and a composite Schmid factor combining the global Schmid factor and geometrical compatibility factor were obtained to better explain the activated twin variants in magnesium alloys. All the above-mentioned Schmid law based criteria and some energy based criteria as well are summarized in this paper. Their applications in evaluating twin variant selection in magnesium alloys are critically reviewed and discussed. [ABSTRACT FROM AUTHOR]