Failures in adaptation of society to global challenges resulting from climate change, including risks of natural disasters, are defined by a combination of ecological and societal factors which result in growing human vulnerability and damages to critical infrastructure and economic sectors. They are attributed to a high extent to loopholes in the emerging system of adaptive governance and human responses at global, national and local levels. Innovative analysis is presented of major trends and approaches to the multidisciplinary problem of solving the problem of societal adaptation to climate change impact with associated transformations of socio-economic, legal, institutional frameworks and multilevel architecture of adaptation climate policy and measures towards sustainability risks reduction. The features and factors in formation of national and global adaptation regimes, innovations in the United Nations system towards overcoming the gaps in implementation of its universal principles and norms, are analyzed. Global North-South interactions in the formation of the international fund for loss and damage are tracked. Major approaches to the contemporary and future design of an adaptive governance system is studied through the assessment of interactions and linkages between climate change, global ice melting, doubling of average rates of sea-level rise during XXI century, flood risks for coastal areas and small island states, packages of adaptation response measures aimed at damage mitigation by vulnerable regions, communities and stakeholders. In this context the role of recent dynamic developments of international regimes governing adaptation to global climate change challenges and societal vulnerability reduction is reflected on the basis of unpacking the major quests in implementation and effectiveness of adaptation policies.