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We provide a comprehensive quantitative analysis of localized and extendedtopological defects in the steady state of 2D passive and active repulsiveBrownian disk systems. We show that, both in and out-of-equilibrium, thepassage from the solid to the hexatic is driven by the unbinding ofdislocations, in quantitative agreement with the KTHNY singularity. Instead,although disclinations dissociate as soon as the liquid phase appears, extendedclusters of defects largely dominate below the solid-hexatic critical line. Thelatter percolate in the liquid phase very close to the hexatic-liquidtransition, both for continuous and discontinuous transitions, in thehomogeneous liquid regime. At critical percolation the clusters of defects arefractal with statistical and geometric properties that, within our numericalaccuracy, are independent of the activity and compatible with the universalityclass of uncorrelated critical percolation. We also characterize the spatialorganization of different kinds of point-like defects and we show that thedisclinations are not free, but rather always very near more complex defectstructures. At high activity, the bulk of the dense phase generated byMotility-Induced Phase Separation is characterized by a density of point-likedefects, and statistics and morphology of defect clusters, set by the amount ofactivity and not the packing fraction. Hexatic domains within the dense phaseare separated by grain-boundaries along which a finite network of topologicaldefects resides, interrupted by gas bubbles in cavitation. The fractaldimension of this network diminishes for increasing activity. This structure isdynamic in the sense that the defect network allows for an unzipping mechanismthat leaves free space for gas bubbles to appear, close, and even be releasedinto the dilute phase.

Unified analysis of Topological Defects in 2D systems of Active and Passive disks