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Pioneering explorations of the two-dimensional (2D) inorganic layered crystals (ILCs) in electronics have boosted low-dimensional materials research beyond the prototypical but semi-metallic graphene. Thanks to species variety and compositional richness, ILCs are further activated as hosting matrices to reach intrinsic magnetism due to their semiconductive natures. Herein, we briefly review the latest progresses of manipulation strategies that introduce magnetism into the nonmagnetic 2D and quasi-2D ILCs from the first-principles computational perspectives. The matrices are concerned within naturally occurring species such as MoS2, MoSe2, WS2, BN, and synthetic monolayers such as ZnO and g-C2N. Greater attention is spent on nondestructive routes through magnetic dopant adsorption; defect engineering; and a combination of doping-absorbing methods. Along with structural stability and electric uniqueness from hosts, tailored magnetic properties are successfully introduced to low-dimensional ILCs. Different from the three-dimensional (3D) bulk or zero-dimensional (0D) cluster cases, origins of magnetism in the 2D space move past most conventional physical models. Besides magnetic interactions, geometric symmetry contributes a non-negligible impact on the magnetic properties of ILCs, and surprisingly leads to broken symmetry for magnetism. At the end of the review, we also propose possible combination routes to create 2D ILC magnetic semiconductors, tentative theoretical models based on topology for mechanical interpretations, and next-step first-principles research within the domain.