Although several modifications to graphene have been proposed to improve its hydrogen binding to practical levels, current theoretical studies largely neglect the role of topological defects. In this paper we analyze the effect of these defects and their possible use in a hydrogen storage system. Hydrogen physisorption on five types of point defects (Stone-Wales, single vacancy and three types of double vacancy) was investigated using density functional theory with the PBE-GGA functional. Point defects were also repeated with the vdW-DF2 functional to better represent long range van der Waals interactions. Although none of the defects were found to be detrimental to hydrogen anchoring, only the single vacancy showed promising hydrogen binding in the ideal range. Model systems combining different defects were also explored, including a defect-anchored metal system, a bilayer graphene system and a grain-boundary system. Finally, two high defect density structures constructed using vacancies and combined Stone-Wales defects and vacancies yielded gravimetric densities of 5.81% and 7.02%, respectively, with the vdW functional. This study suggests that graphene can be defect-engineered to develop effective hydrogen storage media. Copyright (c) 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.