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A key prediction of the SO(5) theory is the antiferromagnetic vortex state. Recent neutron scattering experiment on LSCO superconductors revealed enhanced antiferromagnetic order in the vortex state. Here we review theoretical progress since the original proposal and present a theory of static and dynamic antiferromanetic vortices in LSCO superconductors. It is shown that the antiferromagnetic region induced by the vortices can be greater than the coherence length, due to the light effective mass of the dynamic antiferromagnetic fluctuations at optimal doping, and close proximity to the antiferromagentic state in the underdoped regime. Systematic experiments are proposed to unambiguously determine that the field induced magnetic scattering originates from the vortices and not from the bulk. [Copyright &y& Elsevier]