Our first review article (Wagemans et al., 2012) on the occasion of the centennial anniversary of Gestalt psychology focused on perceptual grouping and figure-ground organization. It concluded that further progress requires a reconsideration of the conceptual and theoretical foundations of the Gestalt approach, which is provided here. In particular, we review contemporary formulations of holism within an information-processing framework, allowing for operational definitions (e.g., integral dimensions, emergent features, configural superiority, global precedence, primacy of holistic/configural properties) and a refined understanding of its psychological implications (e.g., at the level of attention, perception, and decision). We also review 4 lines of theoretical progress regarding the law of Prägnanz-the brain's tendency of being attracted towards states corresponding to the simplest possible organization, given the available stimulation. The first considers the brain as a complex adaptive system and explains how self-organization solves the conundrum of trading between robustness and flexibility of perceptual states. The second specifies the economy principle in terms of optimization of neural resources, showing that elementary sensors working independently to minimize uncertainty can respond optimally at the system level. The third considers how Gestalt percepts (e.g., groups, objects) are optimal given the available stimulation, with optimality specified in Bayesian terms. Fourth, structural information theory explains how a Gestaltist visual system that focuses on internal coding efficiency yields external veridicality as a side effect. To answer the fundamental question of why things look as they do, a further synthesis of these complementary perspectives is required.